After a competitive first half, the Red Devils dominated proceedings in the second period and hit the bar twice.
The league leader opened the scoring through Patrice Evra in the first half, with the France international heading in a corner, but Swansea soon equalized.
After good work from Wayne Routledge and Jonathan De Guzman, Michu tapped in to level the scoring and the club held on for a point, despite United dominating the second half and hitting the bar twice.
The home team made just the two changes from the side which lost to Tottenham in the club's last fixture, as Michel Vorm and Kemy Agustien came in for Gerhard Tremmel and Ki Sung-Yong.
Sir Alex Ferguson also made two changes for the trip to Swansea, both coming at the heart of the defense with Rio Ferdinand and Chris Smalling dropping out of the team for Nemanja Vidic and Jonny Evans.
The match had been built up as a face off between the Premier League’s two top scorers Robin van Persie and Michu, and the Spaniard was the first to get through on goal as he broke away from Jonny Evans inside the first 10 minutes, but his wild effort went well wide.
United, however, soon had the lead as van Persie whipped in an inviting corner from the right and Patrice Evra rose to bag his third goal of the season, diverting the delivery into the far side of the net.
Both sides continued to create chances, but it was Swansea which grabbed the next goal as Jonathan De Guzman fired at David De Gea after a clever Wayne Routledge pass into the area, only for Michu to tap in for his 13th league goal of the season.
Michu’s goal proved a massive confidence boost as the home side began to press for a second. After some rather awful defending by Tom Cleverley, De Guzman stole the ball before shooting, but De Gea managed to catch his effort at the near post.
United created a few attacks late on in the half, but with Antonio Valencia and Ashley Young both having poor matches, supply from the flanks was terrible and the two teams went into the break level.
United began the second half in improved fashion, but Routledge was soon causing trouble again as he produced one step over before shooting straight at De Gea, while Young had an effort blocked at the other end within seconds.
United took control of the midfield around the hour mark, but with the likes of Wayne Rooney and Young looking well off the pace, supply to van Persie and substitute Javier Hernandez was dreadful.
However, Rooney soon produced one excellent to delivery, but the crossbar came to Vorm’s rescue after van Persie’s flick. The Dutchman soon set up Michael Carrick for a chance of his own, but the midfielder’s header came back off the woodwork too, seconds after the disappointing Rooney was hooked for Ryan Giggs.
Sir Alex's men had their host under significant pressure for the final minutes, but with the final ball lacking, Swansea held on for a very commendable point, the club's first ever Premier League point against Manchester United