Robin van Persie was at the heart of both the Reds' early goals as Sir Alex's men raced into a 2-0 lead inside 12 minutes. Chelsea clawed their way back into the game, though, thanks to a goal either side of the break from Juan Mata (free-kick) and Ramires (header).
The Blues then lost Branislav Ivanovic and Fernando Torres to red cards and United's numerical advantage paid off on 75 minutes when Javier Hernandez turned Rafael's shot into the net to secure the three points.
The 3-2 win pulls United to within a point of Chelsea at the top of the table and extends the Reds' winning streak to five games in all competitions.
You can view action and celebration images from the victory by clicking on the photo above.