The former Manchester City midfielder beat Fabien Barthez five minutes before halftime after United had failed to clear a Damien Duff free kick.
United, who had won nine and draw one of their previous 10 games in all competitions since losing 3-1 to Manchester City on November 9, will wonder how they failed to win the game.
They dominated the first half and much of the second in terms of possession but over the 90 minutes Blackburn created the better chances.
The result left United third in the standings on 35 points. Arsenal still lead the way on 39 points after their 2-0 home win over Middlesbrough on Saturday. Chelsea, who beat Aston Villa by the same score at Stamford Bridge, are second on 37.
Newcastle United are fourth on 32 following their 2-0 home win over Fulham. Everton, fifth on 32, visit sixth-placed Liverpool (31) later on Sunday. Blackburn moved up to ninth on 27 points.
The game at Ewood Park took a long time to warm up, though United played some neat football in the early stages.
Ruud van Nistelrooy put one half-chance over the bar after 30 minutes and then forced his way through the Blackburn defence five minutes later but his low shot lacked venom and was comfortably smothered by Brad Friedel.
Blackburn had hardly threatened in the opening 40 minutes but then stunned the visitors by taking the lead.
Duff swung in a deep free kick which defender Martin Taylor nodded back goalwards. United defender Wes Brown headed the ball away but only as far as Rovers skipper Flitcroft who fired a bouncing shot past Barthez from 12 metres.
It was the first goal United had conceded in more than eight hours of play, following five successive clean sheets in three competitions, and it gave Blackburn a real lift for the second half.
It was much livelier after the break and Blackburn went close to a second five minutes after the restart when three players were all inches away from touching in a fizzing low cross by Duff.
There was some good news for United after an hour with the introduction of Roy Keane for his first appearance since August.
The inspirational Irish midfielder, who had undergone hip surgery, was later joined by fellow-substitute David Beckham but neither of the big-name players were able get control of the game.
Van Nistelrooy had the United’s best chance of the match in the 65th minute after a clever flick by Paul Scholes but after Friedel forced him wide, the Dutch striker shot wide.
As United pressed for the equaliser Blackburn began to look dangerous with Flitcroft and former United strikers Andy Cole and Dwight Yorke all missing opportunities for a second goal.
It did not matter in the end though as Blackburn were left to celebrate their first league victory over United since 1995 in the first of three meetings in four weeks between the Lancashire rivals.
They play each other over two legs in the League Cup semi-final in January.
It was the first time in 12 attempts that Flitcroft had been on the winning side against United.
“It was nice,” he told Sky Sports. “I got the old “City reject” shouts in the car park so it was nice to get one back on them.”
Rovers manager Graeme Souness said his team had improved in the second half after a slow start.
“We worked very hard for the result today,” he said.
“I thought we started nervously and showed them too much respect, not getting amongst them in midfield.
“In the second half we started to do that and in the end I thought we caused them a lot of problems.”—Reuters