A pair of penalties helped the Red Devils claim all three points in a dominating performance in Manchester, while City was bested by Everton in a 1-0 defeat at Goodison Park.
Javier Hernandez put United in front from the spot in the 38th minute and Dimitar Berbatov followed suit with a spot-kick goal eight minutes into the second period.
Manchester United controlled much of the first half but struggled to break down a staunch Stoke City defense. It seemed as though the Potters had looked to "park the bus" and settle for a scoreless draw in such a tough atmosphere.
But Ji-Sung Park gave United a golden opportunity to take the lead after he was tripped up in the box by Jermaine Pennant. And as Hernandez converted from the penalty spot, there was a collective sigh of relieve from the Old Trafford faithful.
United grabbed its second, also from the penalty spot, in the 53rd minute after Antonio Valencia was pulled down in the box. Berbatov took the spot kick the second go-around and slotted it home for his seventh goal of the Premier League season.
The Red Devils demonstrated their ability to bounce back from adversity after losing out to Liverpool in the FA Cup at the weekend. United has now won three straight in Premier League play to improve to 54 points.
The Potters, meanwhile, remain in eighth place in England's top flight with 30 points despite losing their second straight contest.
Everton 1, Manchester City 0
Liverpool, England - Darron Gibson kept the title race wide open with a 60th- minute goal at Goodison Park on Tuesday, guiding Everton to a 1-0 win over Manchester City.
The result sees city rivals Manchester United climb level with City for pole position in the Premier League as the two sides are deadlocked on 54 points apiece. Everton, meanwhile, climbs into the top-half of the table where the Toffees are tied with Norwich City on 29 points but edge the Canaries on goal differential.
Swansea City 1, Chelsea 1
Swansea, Wales - Despite the late sending off of Ashley Cole, 10-man Chelsea stormed back to claim a point in dramatic fashion as the Blues played to a 1-1 draw with Swansea City at the Liberty Stadium on Tuesday.
Scott Sinclair put the home side in front just before the break, striking in the 40th minute. And while Cole was dismissed after picking up his second yellow card in the 86th minute, Jose Bosingwa rescued the Blues with a stoppage-time equalizer.
Chelsea has now drawn two-straight Premier League fixtures as it clings to fourth place on 42 points, while Swansea continues to search for a position in the top-half of the table as it sits two points adrift of 10th place on 27 points.
Liverpool 3, Wolverhampton 0
Wolverhampton, England - Liverpool continued its rich vein of form Tuesday with a comfortable 3-0 victory over Wolverhampton at Molineux.
The Reds took all three points thanks to second-half goals from Andy Carroll, Craig Bellamy, and Dirk Kuyt, completing a wonderful week that saw Liverpool advance to the Carling Cup Final at the expense of Manchester City and the fifth round of the FA Cup at the expense of Manchester United.
Wolverhampton remains in the relegation zone on 18 points after dropping its second-straight result, while Liverpool moves into fifth place on 38 points ahead of more Premier League play Wednesday.
Tottenham 3, Wigan 1
London, England - A brace from Gareth Bale helped Tottenham extend its lead above fourth-place Chelsea as Spurs cruised to a 3-1 win over Wigan at White Hart Lane on Tuesday.
Bale opened the scoring in the 29th minute and Luka Modric doubled the lead five minutes later to give the home side a two-goal advantage going into halftime. Bale added a third in the 64th minute before James McArthur pulled one back in the 81st minute.
Tottenham remains third in the Premier League with 49 points, gaining two points on Chelsea after the Blues were held to a 1-1 draw at Swansea. Wigan stays bottom on 15 points with its fourth successive loss.