Juan Mata saw an 87th-minute effort deflected into the back of the net by Phil Jones, sending the Blues back into third place, before Rafael was shown a late red card for kicking out at fellow Brazilian David Luiz.
Although United boss Sir Alex Ferguson insisted there would be no easing off even though the title was won a fortnight ago, it was hard not to notice a slackening in attitude from the hosts.
With Michael Carrick missing, they were forced to look to Ryan Giggs for some incisive passing and it took the veteran Welshman some time to find his range.
In the meantime, both Rafael and Jones burst into the box, only for Petr Cech's massive frame to get in the way.
Just before half-time, Giggs presented Robin van Persie with a decent opportunity when he crossed from the left, only for Cech to again block the route to goal.
The end of season feel was rather at odds with Chelsea's predicament. Europa League finalists may be good for interim manager Rafa Benitez's CV, as Ferguson pointedly noted on Friday, but there is no absolute certainty they will be featuring in next season's UEFA Champions League yet.
Demba Ba put a couple of chances over, as did Victor Moses.
The deadlock should have been broken 15 minutes from time when Frank Lampard picked out Mata with a sublime chip into the box. But, unmarked, the Spain midfielder inexplicably failed to make any contact with his header and Rafael bundled away.
It was all rather humdrum until the final five minutes.
Wayne Rooney felt Ramires had fouled him on the edge of the Chelsea area to win possession in the first place, but once they countered, the visitors always had an extra man.The ball was eventually ferried out to Mata, whose shot may have been creeping in, but definitely did after it flicked off Jones, bouncing in off the post.
United's frustrations boiled over almost immediately as Rafael went through the back of Luiz by the corner flag, believing the Brazilian to have swung an elbow.
Giggs was incensed at Oscar for waving an imaginary card, but after the two sides had been separated, referee Howard Webb did just that, a red one that will mean a three-match ban and an early end to Rafael's season.