Manchester United missed the chance to extend their lead in the title race back to six points as Michu came out on top in the battle of the Barclays Premier League's top scorers at the Liberty Stadium.
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Patrice Evra had given United the lead in the 16th minute as he headed home from a Robin van Persie corner.
But Swansea continued their good record against the top-flight big guns as Michu finished from close range to move clear of Van Persie with his 13th league goal of the season.
United hold a four-point lead over Manchester City at Christmas but will be left to rue a series of missed chances during the final half-hour when they piled the pressure on their hosts.
Swansea felt they had shown United too much respect during this fixture last season but, after a slow start, they showed little sign of being overawed as they took the game to the visitors.
Dwight Tiendalli flashed a threatening ball across the six-yard box before Kemy Agustien freed Michu with a superb long ball, but the Spaniard sliced high and wide.
David De Gea easily saved weak efforts from Wayne Routledge and Michu, but United halted the hosts' building momentum as they took the lead.
Wayne Rooney had already warmed Michel Vorm's hands with a stinging drive before Evra put the visitors ahead, arriving to glance a header in off the far post from a Van Persie corner.
But Swansea recovered well from the blow and Jonathan de Guzman had the ball in the net two minutes later, but the effort was ruled out for Michu blocking off Jonny Evans as the midfielder advanced.
The Liberty Stadium faithful were further angered when Phil Jones was given only a yellow card for a clumsy lunge on Ben Davies, although replays suggested referee Michael Oliver had got the decision right.
But it was United who felt they had been victims of an injustice as Michu levelled on the half-hour mark.
Evra was caught out by De Guzman's clever run and when De Gea could only parry the Dutchman's angled shot, Michu was on hand to tap in.
Sir Alex Ferguson was visibly angered that Van Persie was not awarded a free-kick after he and Chico Flores went to ground following the Spaniard's challenge seconds before the equaliser, and the United boss made his feelings known to referee Oliver at the break.
The goal added an extra bite to Swansea's play and they had the better of the remainder of the opening half.
De Guzman and Routledge were becoming increasingly influential for the hosts and the former should have done better after working his way into the United box on the byline, only to shoot straight at De Gea with several team-mates well placed.
But United offered a remainder of their quality in first half stoppage time when Evra easily got past Nathan Dyer and intelligently pulled the ball back to Rooney, but the England forward fired directly at Vorm.
The second half started at a furious pace and there were chances for both sides.
Michu again headed over and De Gea had to stand firm to repel Routledge's close-range strike.
At the other end Ashley Williams made two superb blocks to stop goalbound efforts from Rooney and Ashley Young after Swansea twice surrendered possession cheaply.
United were finally exerting some authority and Van Persie came close to putting them back in front as he cleverly diverted a Rooney cross goalwards, only to see his effort cannon away off the bar.
Substitute Javier Hernandez wasted another presentable chance as he failed to control Van Persie's astute pass and Vorm gratefully held the Mexican's deflected strike.
Worse was to follow for United when Rooney dispossessed Chico Flores but allowed the defender to get back and intercept a slack pass which should have given Hernandez an easy finish, much to the fury of his manager.
Tempers flared as United frustrations grew. Van Persie was struck on the head by a Williams clearance after being brought down on the edge of the box leading to some pushing and shoving and a booking apiece for the central protagonists.
Swansea were by now under incessant pressure.
Vorm tipped a Carrick header against the bar while Van Persie and Young were denied by blocks from Williams and Davies, although there was a suspicion of handball about the latter, as Swansea held out.