...and they did. David Moyes can afford to smile a little after his United side got noticeably stronger over 90 minutes. That's not happened enough times this season...
As long as there is both football and human weakness, there will be allegations of match-fixing. But a decent start would be an independent, national body...
* First things first - it wasn't a great match. Arsenal and Liverpool have been involved in some captivating battles over the years, but this was a rather scrappy affair pock-marked by individual errors. Both teams fought hard to get a foothold in the game, but Arsenal soon realised that they had the quality to pick Liverpool off on the break and one goal always looked like being enough to secure all three points. A second brought Santi Cazorla the recognition his recent performances have deserved.
* Before the match Brendan Rodgers spoke about how he can learn from a manager as experienced as Arsene Wenger, and Le Prof provided another lesson at Anfield as his team refused to let Liverpool settle into the rhythm they found against Man City. With a front four of Cazorla, Lukas Podolski, Olivier Giroud and Alex Oxlade-Chamberlain hassling and harrying Liverpool's defence and Pepe Reina, the Reds struggled to get into their stride and looked rushed in possession and even a little bit nervous.
Wenger's tactic to press Liverpool high up the pitch in the early stages was reminiscent of Everton's approach against Rodgers' Swansea at the Liberty Stadium last season. It worked on that occasion, with the Toffees' pocketing a 2-0 victory, and it helped Arsenal replicate the scoreline on Sunday.
* Individual errors played a big part in the game and while Arsenal made their fair share, Liverpool's proved to be more costly. While Nick Miller succinctly pointed out that Andy Carroll just fits into Sam Allardyce's West Ham team, Steven Gerrard stands out like a sore thumb in Rodgers' Liverpool line-up. The captain was again sloppy in possession, whacking 13 balls into the Arsenal box with only three finding a team-mate, and it was his error that led to the Gunners' opening goal. The elephant in the room has just farted, and it's Rodgers' job to open the window.
* Gerrard typified Liverpool's problem of trying to be too direct at many stages during the match. Sideways passes may be criticised by some, but the Reds will have to learn the art of patience if they are to reap the rewards of Rodgers' teaching. Apart from obvious errors, they exuded a calmness in their performance against Man City. Sunday was a backwards step.
* Not only is Gerrard becoming an increasing problem for Rodgers, but Reina has now made three key errors in the space of a week. The 'keeper spent all afternoon against Man City flapping at crosses - including the delivery that resulted in Yaya Toure's equaliser - and spilled David Templeton's shot into his own net to give Hearts the lead at Anfield on Thursday. He should have done a lot better with Cazorla's drive that made it 2-0 to Arsenal and Rodgers will be worried about the Spaniard's form. Anders Lindegaard replaced David De Gea in nets for Man United's trip to Southampton - perhaps Reina is suffering from the lack of a similar level of competition at Anfield.
* After Martin Skrtel's howlers against West Brom and Man City, I suggested that 'bemused' has been the centre-back's only facial expression since Rodgers' arrival and introduction of a new system. However, the 27-year-old looked improved alongside the returning Daniel Agger and was excellent in his use of the ball. Although the day ended in defeat, there were signs that Liverpool's central pairing are gradually adjusting to Rodgers' changes.
* Of course, Arsenal's defence deserves considerable credit for keeping a third clean sheet in a row. With Steve Bould's methods having an instant effect on the Gunners' defensive fortunes, one wonders why the new assistant manager hasn't had more involvement in first-team affairs previously. His help was certainly needed last season when Arsenal stumbled to their worst defensive record for 28 years.
* The big issue for Liverpool at the moment - and until January, at least - is the self-inflicted lack of strikers that left Stewart Downing, supposedly a left-back, as the most attacking option on the bench. By his own admission Rodgers is a 'nutcase' for allowing Andy Carroll to leave on loan without bringing in a replacement and as tumble weeds rolled through Anfield on deadline day, you have to wonder what on earth Ian Ayre and co were doing.
The absence of any activity has left the Reds worryingly short and youngsters such as Adam Morgan will be required to help out as the team battles on four fronts until the next transfer window. To add to concerns, Morgan wasn't even deemed worthy of a place in the squad for the Arsenal match.
* Furthermore, Liverpool's first-choice forwards - Luis Suarez and Fabio Borini - are hardly the ideal poachers required to banish the memories of last season's profligacy. Sarah Winterburn likened Borini to Dirk Kuyt following the 2-2 draw with Man City, but so far the striker has been less hard-working and more wasteful than the Dutchman. Indeed, the way he blazed three shots over and wide on Sunday made one yearn for Kuyt - who, incidentally, has scored six goals in seven matches for Fenerbahce - and his maturity in possession.
I've said before that it was rather strange for Liverpool to lump over £10million of their meagre transfer budget on a striker who had only played in 46 professional matches before this season, simply because Rodgers was impressed with Borini during their brief time together at Swansea.
* While Borini is already looking like a costly gamble - given Liverpool's lack of funds - Suarez has improved not one iota since his frustrating contribution last season. Usually the Uruguayan is capable of wriggling into space only to miss a gilt-edged chance, but on Sunday even the wriggling part went wrong. On several occasions he tried to dribble around Thomas Vermaelen and Per Mertesacker but was stopped dead in his tracks by the Arsenal pair, who had an impressive afternoon.
Suarez had a shout for a penalty when Mertesacker foolishly put a hand on his shoulder (which brought a dramatic tumble) in the second half, but that doesn't excuse the striker's failings. I agree with the school of thought that Suarez would be best cutting in from the left wing, but with Rodgers left with no other options for the central role, we're likely to see him continue where he is for now, much to the team's detriment.
* Liverpool were perhaps not the only team to provide evidence of a striker shortage on Sunday, as Olivier Giroud again looked short of quality in Arsenal's front line. Indeed, those of us who were instantly attracted to Giroud and his lean torso are gradually becoming deterred by the stench coming from the Frenchman's shooting.
Giroud was presented with a brilliant opportunity to put Arsenal 2-0 ahead when Abou Diaby strode forward before half-time and, considering the chance was on his stronger foot, he really should have done better. If the 25-year-old doesn't find his shooting boots soon, Wenger may have to push Podolski into the centre and start Theo Walcott on the left. That, or he could always turn to Marouane Chamakh.
* With Cazorla and Oxlade-Chamberlain buzzing all over the place and Diaby willing to open his legs at the right opportunity, Arsenal looked a lot quicker than Liverpool, especially in central areas. Liverpool have speed in Sterling and Suarez, but they often looked slow and sluggish in midfield, exemplified by Nuri Sahin running through quicksand as he tried to catch Cazorla in the build-up to Podolski's opener.
* Raheem Sterling was Liverpool's brightest attacking threat for most of the match. The 17-year-old has pace to burn, and is rapdily learning when to use it on the outside of the full-back and when to look inside for a pass or for space to exploit. Considering his impressive performances, and that Liverpool are light on numbers, Sterling will play a key role in the team's fortunes until January. Let's hope he doesn't break under the unexpected pressure.
* While Sterling was involved in the positive aspects of Liverpool's play, Abou Diaby was hugely influential for Arsenal. Wenger may be derided for his persistence with Diaby - with the midfielder spending more time in the treatment room than on the pitch over the last two seasons - but on days like Sunday you can see why the Arsenal manager has faith in the 26-year-old.
The Frenchman was a thorn in the side of Liverpool all afternoon and his driving run towards the end of the first half should have brought a goal from Giroud. Mikel Arteta was the only Arsenal player with a better pass completion rate than Diaby (excluding late subs), while the injury-prone midfielder also weighed in with four important tackles and three interceptions. After reminding us all of his talent, hopefully Diaby can remain fit for the foreseeable future.
* A quick glance at John Henry's Twitter timeline reveals the frustration and anger of many Liverpool fans over the club's failure to bring in a new striker. But now is not the time to vent collective rage; the new team and new manager need to be given a chance until January. If shortcomings are not addressed at that stage, then by all means crank up the pressure.
* Rodgers should really stop sitting on the little wall in front of the dug-out. He's only setting himself up for 'Humpty Dumpty Has A Great Fall' headlines when/if he's eventually sacked.
Matt Stanger - he's on the Twitter.