Diniyar Bilyaletdinov headed the rebound to force goalkeeper Andreas Isaksson into a diving save.
Liverpool finally found some rhythm and David Ngog had a chance to equalise but headed straight at Andreas Isaksson.
Gerrard should have put the match away in stoppage time, but he shot straight at Isaksson, wasting a three-on-one breakaway.
Berg fired wide after the break and PSV keeper Andreas Isaksson saved well from Kyle Bartley's header for the visitors.
Isaksson then turned over a rising drive from Giggs as United threatened to take advantage of City's need to push forward.
BBC: Wayne Rooney celebrates putting Man Utd ahead in the derby
At the other end, Villa jumped on Silva's rebound in the 63rd minute and fired straight at Isaksson from close range.
Fabregas saw a superb 30-yard strike well parried by City keeper Andreas Isaksson as the Gunners continued to pile on the pressure.
He got round the back of left-back Michael Ball as he chased a Steven Gerrard pass only to see his stabbed shot saved by Isaksson.
Wenger's side nearly retook the lead when first Emmanuel Adebayor's effort was well saved by Isaksson and then Alexander Hleb flashed a left-footed strike just wide.
Seconds after Isaksson had denied Terry with a miraculous close-range save, he was beat by a shot straight down the middle of the goal from Walcott.
Saha missed a glorious chance to add United's third after 52 minutes, but he shot wildly over the top after Isaksson could only block Rooney's shot.
BBC: Wayne Rooney celebrates putting Man Utd ahead in the derby
But England hit back when an Ashley Young corner was cleared straight to Walcott, whose 20-yard strike deceived Isaksson and flew into the middle of the net.
Their pressure resulted in a string of corner kicks but no clear opportunities until Yuri Zhirkov's hard volley in the 21st went just outside Isaksson's left post.
Uniyed had not been at their best, but Rooney was a constant threat, forcing a diving save from Isaksson with an instant left-foot shot on the run.
BBC: Wayne Rooney celebrates putting Man Utd ahead in the derby
Isaksson was in action again two minutes later as United started to produce flashes of their trademark passing game, denying Rooney at point-blank range from Giggs' cross.
BBC: Wayne Rooney celebrates putting Man Utd ahead in the derby
Still, however, the Sweden defence allowed Laizans space and when the ball broke to him after 26 minutes, his deflected shot left the sprawling Isaksson with no chance.
Adebayor was then denied twice inside three minutes - the first by a brilliant block from Sylvain Distin before Isaksson got down to keep out his powerful header.
Isaksson quickly gathered and hoofed the ball up the park as Rangers players complained in vain to the multitude of match officials who had failed to spot the infringement.
Edu was well placed to level the game on the hour when a Whittaker flick-on found him near the penalty spot but the American shot tamely at the advancing goalkeeper Andreas Isaksson.
The Englishman was left clutching his left knee after a collision with PSV Eindhoven's Swedish goalkeeper, Andreas Isaksson, with just a few minutes of the 1-0 defeat left to play at Ibrox.
BBC: Rangers' Kyle Bartley misses cup final with knee injury
But both sides kept up the entertaining pace and Heskey's replacement, Ryan Taylor, broke free down the left to connect with a deep Melchiot cross forcing a strong save from City keeper Andreas Isaksson.
At the other end, Laizans twice served notice of his danger, first firing wide from 20 yards, then bringing a fine save from Sweden stopper Andreas Isaksson, who turned the ball out for a corner.
Roy Hodgson's side were on top in the first half and their pressure told when Steven Gerrard sent an inch-perfect cross into the box for Carroll to plant a trademark bullet header past Andreas Isaksson.
Urby Emanuelson made it 3-3 with a shot from the edge of the area that beat Isaksson at his near post eight minutes later, but Bakkal crashed in the winner from 10 yards in the 75th minute after defender Jan Vertonghen failed to head clear.
Villa was in the team despite sustaining a hairline fracture of his right index finger while celebrating the first of his hat-trick goals against Russia, and the Sweden defense kept him under wraps until the 38th minute, when Isaksson had to stop a low shot.
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