City edged Tottenham earlier in the day to see the Citizens extend their lead atop the table to six points, but United kept pace by claiming three points in North London against the Gunners. City leads on 54 points, followed by United on 51 points and Tottenham on 46 points. Arsenal is tied with Newcastle for fifth place on 36 points apiece.
Antonio Valencia put United in front just before the break, while Robin van Persie grabbed his 19th goal of the Premier League season to equalize. Danny Welbeck went on to steal a late winner just nine minutes from time.
Manchester United controlled much of the opening period, but did not go in front until first-half stoppage time.
Ryan Giggs was given the freedom on the left wing to collect possession and pick out his cross. His pinpoint delivery was met by Valencia at the back post where the Ecuadorian midfielder guided his header into the back of the net.
Arsenal came out gunning in the second half and quickly created several scoring chances, but failed to finish them off.
The Gunners nearly capitalized on a slip from United defender Chris Smalling, but van Persie sailed his close-range effort wide of the post.
Alex Oxlade-Chamberlain came within inches of netting a stunning equalizer when he unleashed a low shot from outside the box in the 62nd minute, but it skimmed just wide of the post.
Moments later, United nearly grabbed a second when Welbeck got free on goal. He slipped a shot past an on-rushing Wojciech Szczesny, but Per Mertesacker tracked back and cleared the ball off the line.
The Gunners finally got their equalizer, and it came in typical Arsenal fashion.
Laurent Koscielny started the counter-attacking move in his own box with a pass to midfield. The move culminated in a brilliant through-ball from Oxlade- Chamberlain to pick out van Persie. The Dutch striker turned and shot in one motion as his effort struck the far post and went into the back of the net.
But Arsenal was only level for 10 minutes. Valencia made a darting run into the box from the right wing, and after a quick one-two, he picked out Welbeck with a square pass played in front of goal. Welbeck calmly slotted the ball past Szczesny with a one-time effort to hand United the win.
Manchester City 3, Tottenham 2
Manchester, England - Manchester City preserved its first-place position in the Premiership table in dramatic fashion Sunday, edging third-place Tottenham, 3-2, at the Etihad behind late penalty kick from Mario Balotelli.
A scoreless opening period gave way to a back-and-forth spell in the second half as the two sides traded a total of four goals in the span of nine minutes.
Samir Nasri gave City the lead in the 56th minute and Joleen Lescott added to that advantage three minutes later, but Tottenham leveled quickly through Jermain Defoe in the 60th minute and Gareth Bale in the 65th minute.
The thrilling match concluded when Balotelli was tripped up in the box. The Italian striker converted the ensuing penalty kick in second half stoppage time to help ensure that City remains top of the table.
City has now won three-straight Premier League matches, improving to 54 points on the year.
Tottenham sees its seven-game unbeaten run come to an end as the North London club remains in third place on 46 points.