United missed the chance to go top as 20/1 outsiders Blackburn lifted themselves from the foot of the table after claiming four points from their last two away games.
Ayegbeni Yakubu beat United goalkeeper David De Gea from the penalty spot in the 16th minute to put Blackburn in front after Dimitar Berbatov hauled down Christopher Samba in the box.
The Rovers striker scored again six minutes into the second half when he beat Michael Carrick and Phil Jones and buried a powerful shot past De Gea.
However, United hit back straight from the restart when Patrice Evra's cross found Rafael, whose mis-hit shot was headed home by Berbatov from six yards, and Berbatov added his second in the 62nd minute from Antonio Valencia's cross.
But Blackburn regained the lead with 10 minutes left on the clock after a howler from De Gea, who failed to claim Morten Gamst Pedersen's corner which was headed into the back of the open net by Rovers defender Grant Hanley.
Didier Drogba scored his 150th goal for Chelsea from the penalty spot but it was not enough as the Blues lost 3-1 to Aston Villa at Stamford Bridge.
The Ivory Coast international capitalised after he was fouled by Richard Dunne and stepped up to coolly beat Brad Guzan, who dived the right way but just over the top of the striker's spot-kick.
Stephen Ireland hit back for Villa five minutes later before Stiliyan Petrov gave Villa the lead in the 83rd minute. Ireland then unselfishly played in Darren Bent for Villa's third three minutes later.
Tottenham drew 1-1 against Swansea at the Liberty Stadium to reduce the gap to second-placed United to six points.
Rafael Van der Vaart scored the opener with a close range volley in the first half before Swansea levelled after the break when Scott Sinclair capitalised on a goalkeeping error by Brad Friedel.
Friedel failed to claim Angel Rangel's deflected cross, allowing Sinclair to poke home into the open net.
Robin Van Persie's second-half strike gave Arsenal a 1-0 win over QPR at the Emirates after the Gunners missed several chances in a frustrating match.
The Dutchman struck home in the 60th minute after Andrey Arshavin played him through on goal with an inch-perfect pass to allow the forward to drill a left-footed shot past QPR keeper Radek Cerny. It was Van Persie's 35th Premier League goal of 2011, just one short of Alan Shearer's record for a calendar year.
Stoke drew 2-2 against 10-man Wigan in an all-action game at the Britannia Stadium.
Victor Moses gave Wigan a slender lead at half time before the Latics were reduced to 10 men and conceded a penalty when Gary Caldwell was dismissed for deliberate handball in the 76th minute.
Jonathan Walters stepped up and converted the resultant penalty before Cameron Jerome gave Stoke the lead after a brilliant piece of skill by Peter Crouch and an assist by Walters.
However, Wigan were level just three minutes later when Ryan Shotton fouled Hugo Rodallega in the area, with substitute Ben Watson scoring the penalty with his first touch of the game.
Elsewhere, Bolton drew 1-1 against Wolves at the Reebok. Returning defender Sam Ricketts opened the scoring in the 22nd minute before Wolves striker Steven Fletcher levelled the score after the break when he nodded home Matt Jarvis' free-kick at the far post in the 49th minute.
Elsewhere, Simeon Jackson's stoppage-time header earned a point for Norwich as they claimed a 1-1 draw against Fulham at Carrow Road.
Orlando Sa opened the scoring for Fulham in the seventh minute when he wriggled free on the edge of the box and fired past John Ruddy and into the bottom corner of the net.
However, Jackson claimed a point for Paul Lambert's side when he headed home Elliott Bennett's cross in the fourth minute of stoppage time.
Premier League Saturday Results
Man United 2-3 Blackburn
Chelsea 1-3 Aston Villa
Arsenal 1-0 QPR
Swansea 1-1 Tottenham
Bolton 1-1 Wolves
Norwich 1-1 Fulham
Stoke 2-2 Wigan