With leaders Manchester City not playing until Sunday against Sunderland, United went 2-0 down after two goals by Yakubu Aiyegbeni. Dimitar Berbatov scored twice to bring the champions level before Grant Hanley's 80th-minute winner stunned Old Trafford.
City were the day's big winners as the chasing pack dropped points, Chelsea losing 3-1 at home to Aston Villa and Tottenham Hotspur conceding a late goal to draw 1-1 at Swansea City.
Arsenal jumped above Chelsea into fourth place after Robin van Persie netted his 35th league goal of the calendar year in a 1-0 win at home to Queens Park Rangers.
United have 45 points from 19 games and trail City on goal difference before Roberto Mancini's side travel to Sunderland. Spurs are third with 39 points, having played one game fewer than United, while Arsenal have 36 and Chelsea 34.
"Obviously it's a disappointment... we never expected that," United manager Sir Alex Ferguson told ESPN television. "We lost two terrible goals, you can't do that in games like this."
There had been a party atmosphere in the day's early match at Old Trafford as the crowd sang "Happy Birthday" to the 70-year-old Ferguson but the mood soured in the 16th minute when Berbatov grabbed Rovers defender Chris Samba's shirt and pulled him down.
Referee Mike Dean pointed to the spot and Yakubu sent keeper David de Gea the wrong way.
As if to prove it was no fluke Yakubu extended Blackburn's lead six minutes after the break when he shrugged off challenges by Phil Jones and makeshift centre back Michael Carrick to shoot past De Gea.
Blackburn fans were still celebrating the goal when Berbatov headed in Rafael's mis-hit shot to raise hopes of a United comeback.
BELOW-STRENGTH SIDE
The Bulgarian striker, who hit five goals in this fixture last season, found the net again just after the hour when he turned in an Antonio Valencia cross.
United, fielding a below-strength side due to injuries but welcoming back fit-again midfielder Anderson, continued to press forward before a blunder by De Gea destroyed his team's revival.
The Spanish keeper came out to meet a Morten Gamst Pedersen corner but Hanley beat him to it and the 20-year-old defender headed in to lift Blackburn off the bottom of the table to 19th.
With news of United's defeat known before the other games kicked off, Spurs and Chelsea had every incentive to capitalise on the slip-up by Ferguson's team.
Spurs went ahead at Swansea through Rafael van der Vaart's 44th-minute effort before visiting keeper Brad Friedel failed to hold Angel Rangel's cross and Scott Sinclair equalised in the 84th.
Chelsea also went in front at Stamford Bridge, striker Didier Drogba notching his 150th goal for the club with a 23rd-minute penalty, but Villa equalised five minutes later through Stephen Ireland.
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