Snowy weather had forced the postponements of games against Fulham and Blackpool, meaning the Reds had not played in the league for 18 days.
That showed as they lacked invention and energy - even with the return of Steven Gerrard from six weeks out - but the visitors did have that spark and ended a run of six successive defeats away from home thanks to Stephen Ward's first Premier League goal.
The last time Wolves won at Anfield was 27 years ago next month when Steve Mardenborough scored the only goal of his Wanderers career.
But there could be no complaints from the home side who did not do nearly enough to extend a six-match unbeaten home record stretching back to their fateful loss to newcomers Blackpool on October 3.
Those were the dark days of the Reds' campaign, when they were lingering in the relegation zone after their worst start for 57 years.
Roy Hodgson cannot afford a return to those times with his side 12th in the table and owners New England Sports Ventures still deciding how much money they are willing to give the manager to strengthen the squad in next month's transfer window.
All but Martin Skrtel, Sotirios Kyrgiakos and Dirk Kuyt, had not seen any competitive action since the 3-1 defeat at Newcastle on December 11.
The aforementioned trio had played small parts in the goalless Europa League draw at home to Utrecht but the rest had spent the last two and a half weeks training at Melwood.
It was not apparent from this display as there was a lack of cohesion and fluidity which Wolves were only too happy to take advantage of.
The minute's applause for former Liverpool defenders Avi Cohen, who died aged 54 after a motorbike accident, and Bill Jones - grandfather of Reds right-back Rob Jones - who passed away aged 89 - had barely faded away before Raul Meireles had a chance to put the hosts ahead.
Maybe the lack of match practice contributed to his failure to open the scoring after just seven minutes but it was a poor excuse if so.
Fernando Torres' quickly-taken free-kick left George Elokobi floundering but the Portugal international shot straight at goalkeeper Wayne Hennessey and Richard Stearman cleared the loose ball.
Liverpool's strikers fed on scraps throughout - Torres did not have one opportunity - as Wolves pressurised the man in possession and defended solidly.
David Ngog's left-footed shot from 25 yards was easily claimed by Hennessey as Liverpool struggled to break down Wolves, who were enjoying plenty of possession themselves.
With the visitors finding room on their left it prompted a tactical switch, with Gerrard moving to the right and Meireles returning to the centre where he had enjoyed his best performances.
It lasted only until half-time as Gerrard reverted to the middle.
Again the Reds could have taken an early lead as Dirk Kuyt's pass to Glen Johnson inside the penalty area set up Ngog but he hooked wide from six yards.
Wolves defender Ronald Zubar was slightly closer with his shot on the turn as he at least forced Jose Reina, on his 200th Premier League appearance, into a low save.
It was an omen of things to come as in the 56th minute the visitors took the lead after a mix-up between Skrtel and Kyrgiakos allowed Sylvan Ebanks-Blake's through-ball to squeeze between them.
Ward raced in behind to poke home the first goal conceded at Anfield in 478 minutes in all competitions.
Ngog was replaced by Ryan Babel just past the hour, a decision met with derision by the Kop - who not for the first time this season briefly chanted the name of Kenny Dalglish.
Liverpool were wobbling and only a last-gasp block by Johnson prevented Jarvis making it 2-0.
Hodgson's final two substitutions sent on Joe Cole and Fabio Aurelio for Meireles and Paul Konchesky.
Two minutes from time Skrtel headed in Gerrard's free-kick but he was well offside.
Wolves fans sang "How bad must you be? We're playing away" and on the night it was difficult to argue with that.
The Kop appeared to be in agreement, responding with "Hodgson for England".