The Gunners overcame Fulham 2-0, thanks to two late strikes from Santi Cazorla, whilst City secured a 4-2 success against Cardiff City at the Etihad.
Cazorla was indeed the match-winner at the Emirates as, after a goalless first half, the Spaniard took control.
His first came on 57 minutes as he lashed the ball home from 12 yards after good work from Jack Wilshere and Olivier Giroud.
Just five minutes later and the three points were secured as he fired home from the edge of the box, just putting the ball out of Maarten Steklenburg's reach.
If Arsenal's win was far from convincing, then free-scoring Man City had a surprisingly tough day against Cardiff - despite the scoreline suggesting otherwise.
City dominated the early stages and they went ahead after just 14 minutes after great work from David Silva saw him pull the ball back for Edin Dzeko to dispatch, although goal-line technology was called in to give the goal.
Suddenly Cardiff came to life and they levelled on the half-hour mark through Craig Noone. Aron Gunnarsson slipped a great ball inside and Noone cut in past Vincent Kompany and finished at his near post.
City restored the lead just before the interval and there was a touch of luck about Jesus Navas's goal as Steven Caulker made a good block on Edin Dzeko, but the clearance bounced into the stride of the Spaniard and he slammed it home.
Both sides had chances in the second half, and Joe Hart had plenty of work to do to keep City ahead - but City's class told in the end as they eased to the three points thanks to a further two goals.
Firstly a classic counter-attack saw Yaya Toure stroke the ball home and then the returning Sergio Aguero fired home on his comeback appearance.
There was time for Fraizer Campbell to add another in injury time and it was some consolation for Cardiff who turned in a good display.
Liverpool were unable to strengthen their grip on fourth spot, but recovered from two goals down to draw 2-2 with Aston Villa at Anfield.
Villa had sprung a surprise on their last visit to the red half of Merseyside, and looked like repeating those heroics as they surged in front.
Andreas Weimann tapped home the opener before Simon Mignolet badly misjudged a cross from Gabriel Agbonlahor and Christian Benteke stooped to nod into an empty net.
Liverpool grabbed a lifeline in first-half stoppage-time, with Jordan Henderson cleverly flicking into the path of Daniel Sturridge to produce a composed, chipped finish.
Parity was restored eight minutes into the second half, with Luis Suarez tumbling over a sliding Brad Guzan and Steven Gerrard making no mistake from the penalty spot, but there was to be no thrilling finish for the hosts.
Away from the top, and there were some huge results at the bottom.
The day's early kick-off saw Sunderland mount an excellent comeback which saw them claim a 2-2 draw with Southampton.
The Saints dominated the opening 45 minutes and raced into a two-goal lead thanks to Jay Rodriguez and a clinical finish from Dejan Lovren.
Sunderland replied, though, straight after Lovren's goal when Fabio Borini fired home with their first shot of the game. The leveller then came 19 minutes from time as Adam Johnson smashed into the top corner, although Artur Boruc will feel he could have done better with both goals.
The game was marred late on by two serious-looking injuries for Soutampton as Lovren and second-half substitute Gaston Ramirez were stretchered off.
But the big movers of the day were Crystal Palace as they climbed off the bottom of the table and up to 16th in the table with their 1-0 win over Stoke City at Selhurst Park.
On a day which will no doubt live long in the memory of Tony Pulis - the winner came just after the break.
Oussama Assaidi gave away the ball in his own box, Jason Puncheon picked it up and got the better of Marc Wilson and curled the ball past Jack Butland.
Palace's climb up the table came courtesy of the defeats for Cardiff, Fulham, Sunderland and also West Ham - who lost 3-1 at home to Newcastle United.
Newcastle went ahead 16 minutes in as Yohan Cabaye finished neatly into the corner after good work from Yoan Gouffran.
Newcastle doubled their lead just after the half-hour as Loic Remy took down a cross from Moussa Sissoko in the six-yard box and fired past Adrian.
West Ham got themselves back into the game just before the break when Tim Krul failed to deal with a cross and Carlton Cole looked to poke it home, but it went in off Mike Williamson.
Newcastle wrapped up the win in the final minute when Cabaye added his second with a curling free-kick which was too good for Adrian to keep out.
Hull City remain in 10th, but Norwich City gave their survival hopes a huge boost as they grabbed a 1-0 win at Carrow Road.
The winner came just three minutes from the end as Ryan Bennett rose to meet a Robert Snodgrass corner and seal the win.
Hull's day went form bad to worse late on as Tom Huddlestone saw red for a second yellow card in injury time.