Kean has long been on the hot seat with Blackburn entering the match in last place, but Saturday's vital win may have bought him some more time to turn things around as the club looks to avoid relegation.
A brace from Aiyegbeni Yakubu powered Blackburn to a two-goal lead before United came storming back with two goals from Dimitar Berbatov. With the equalizer, it seemed as if the home side would go on to grab a winner late on, but Scottish defender Grant Hanley stole three points for the visitors with a goal 10 minutes from time.
Blackburn went in front in the 16th minute following a foul in the box. Berbatov pulled down Christopher Samba in the penalty area and Yakubu converted from the spot to give Blackburn the lead against the run of play.
Yakubu then doubled the advantage in the 51st minute, captializing on some slack United defending to get through on goal and hammer a shot between the legs of goalkeeper David De Gea.
United responded immediately as Rafael Da Silva's close-range cross one minute later was met with diving header from Berbatov, who found the back of the net to rejuvenate the crowd and keep the Red Devils in the game.
The Bulgarian striker bagged another goal 10 minutes later, stuffing home a centering pass from Antonio Valencia. All six of Berbatov's goals have come in United's last three Premier League games.
United continued to press in search of a winner, but with ten minutes remaining, the match turned back in favor of visiting Blackburn.
A corner kick sent into the box was not properly dealt with by De Gea and Hanley took advantage, winning the initial header and slotting the ball over the line to leave United with a mountain climb in the closing minutes.
The Red Devils could not conjure another equalizer, and Hanley's goal turned out to be the winner.
The loss snaps a five-game winning streak and nine-game unbeaten streak in league play for United. The Red Devils still remain tied for first place in England's top flight, although Manchester City would go top with a draw or win against Sunderland on Sunday.
With Bolton playing to a 1-1 draw against Wolverhampton, Blackburn climbs out of the cellar but still remains in the relegation zone on 14 points.
London, England - Aston Villa piled on the misery for Andre Villas-Boas as the Villains earned a 3-1 victory over Chelsea at Stamford Bridge on Saturday.
The Blues are winless in their last four Premier League contests, and with owner Roman Abramovich's track record of high manager turnover, Villas-Boas could be on the hot seat.
Chelsea initially took the lead with a penalty kick from Didier Drogba in the 23rd minute, but it was quickly canceled out by Stephen Ireland's strike five minutes later.
The two sides remained deadlocked until the 83rd minute when Stiliyan Petrov slotted home the game-winner. Darren Bent added a third just three minutes later after a giveaway at midfield from Frank Lampard.
Chelsea drops to fifth place on 34 points following Arsenal's 1-0 win over QPR on Saturday, while Villa improves to 23 points to occupy ninth place.
Arsenal 1, QPR 0
London, England - Robin van Persie continued his season-long goal-scoring tear with the lone strike in a 1-0 win over QPR at the Emirates on Saturday.
The Dutchman fired Arsenal into fourth place with his goal in the 60th minute, as the Gunners jumped ahead of Chelsea in the Premiership table following its 3-1 home loss at the hands of Aston Villa.
Van Persie leads the Premier League in goals to this point in the campaign, netting 17 times in the first half of the season.
QPR is winless in its last seven league contests and sits one spot above the relegation zone with 17 points.
Swansea City 1, Tottenham 1
Swansea, Wales - Scott Sinclair notched a late equalizer to see Swansea City salvage a point in a 1-1 draw with Tottenham at the Liberty Stadium on Saturday.
Rafael Van der Vaart had put Spurs in front just before halftime with his seventh goal of the season, but Sinclair helped draw Swansea level with a goal six minutes from time.
Swansea has drawn two straight and is slowly slipping into a battle against relegation. It sits five points above the drop zone with 20 points.
Tottenham remains in third place with 39 points, but fails to take maximum points in an effort to close the gap at the top of the league after Manchester United was stunned by Blackburn earlier in the day.
Norwich City 1, Fulham 1
Norwich, England - Norwich City claimed a dramatic point at Carrow Road on Saturday, playing to a 1-1 draw with Fulham.
Orlando Sa popped up in the seventh minute for Fulham, recording his first goal for the club, but Simeon Jackson rescued Norwich with a goal in second- half stoppage time.
The Canaries are winless in their last four league games and sit 10th in the table with 22 points, two points ahead of the Cottagers who have drawn two straight.
Bolton 1, Wolverhampton 1
Bolton, England - Bolton and Wolverhampton traded goals on opposite sides of halftime as the two sides played to a 1-1 draw at the Reebok Stadium on Saturday.
Sam Ricketts gave the home side the lead with a goal in the 22nd minute, but it was overturned by Steven Fletcher's eighth goal of the season in the 49th minute.
The result does not help either side, as they were both in need of three points as they fight relegation. Bolton, on 13 points, falls to last place following Blackburn's win at Old Trafford, while Wolverhampton, on 17 points, has drawn three straight and is winless in its last five league games.
Stoke City 2, Wigan 2
Stoke-on-Trent, England - Stoke City was held to a 2-2 draw against 10-man Wigan in a dramatic match at the Britannia Stadium on Saturday.
Wigan took the lead through Victor Moses in the 45th minute, but the Latics were reduced to 10 men in the 76th minute when Gary Caldwell was issued a red card for a hand ball in the box to deny a scoring chance. Jonathan Walters converted the ensuing penalty kick to bring Stoke level.
Cameron Jerome thought he had given the home side all three points with a goal six minutes from time, but Wigan earned a penalty three minutes later and equalized as Ben Watson scored from the spot.
Both clubs retain their previous positions in the table, as Wigan remains in the relegation zone on 15 points while Stoke stays in eighth with 26 points.