Incoming QPR manager Redknapp was present at Old Trafford, hours after his appointment as the successor to Mark Hughes was confirmed, and he saw his new charges take a shock lead in the 52nd minute.
Kieron Dyer's cross-shot from the left was palmed out by Anders Lindegaard and Jamie Mackie found the roof of the net from close range.
After losing at Norwich City and Galatasaray in their last two outings, United were staring at the prospect of a third consecutive defeat, but three goals in the space of eight minutes saw them roar into the lead.
Jonny Evans headed in the equaliser from close range in the 64th minute and four minutes later, Darren Fletcher marked his first league appearance in over a year by scoring with a thumping header from Wayne Rooney's corner.
Substitute Javier Hernandez then beat QPR goalkeeper Julio Cesar from Anderson's pass in the 72nd minute to kill the game off and lift Alex Ferguson's men two points above Manchester City at the summit.
City are not in action until Sunday, when they visit fourth-place Chelsea and their new interim coach, Rafael Benitez.
"We only played for 10 minutes and those 10 minutes were brilliant. I thought Anderson changed the game for us," said Ferguson, who also praised Fletcher for battling to overcome a career-threatening bowel condition.
"The boy has had a long journey back and he has showed he is back to his best."
Arsenal, bidding to trim the five-point gap that separates them from the top four, play at Aston Villa in the evening kick-off.
Everton were prevented from closing to within a point of Chelsea as Sebastien Bassong netted a last-minute equaliser to earn Norwich a 1-1 draw at Goodison Park.
Steven Naismith had given the hosts the lead with a 12th-minute tap-in before Bassong struck at the death, meeting Wes Hoolahan's deep free-kick with a back-post header.
Earlier, West Bromwich Albion continued their superb start to the season with a 4-2 win at Sunderland that took them up to third place.
Zoltan Gera's curling 25-yarder put the visitors ahead after half an hour's play at the Stadium of Light, before a fumble from Sunderland goalkeeper Simon Mignolet gifted Shane Long the Baggies' second.
Romelu Lukaku's 81st-minute penalty made it 3-1 after Craig Gardner had scored with a deflected free-kick, but Stephane Sessegnon brought Sunderland back into the game again with a late strike from close range.
However, Steve Clarke's men struck again in injury time through substitute Marc-Antoine Fortune to secure a fourth straight league win.
"To talk about European football at this stage would be folly," warned West Brom coach Clarke.
"There are a lot of games to go, so we'll keep our feet on the ground."
Wigan Athletic prevailed 3-2 at home to fellow relegation contenders Reading after Jordi Gomez completed a hat-trick with an injury-time winner at the DW Stadium.
Reading looked to have snatched a point in the 80th minute when Wigan goalkeeper Ali Al Habsi allowed Hal Robson-Kanu's deflected shot to squirm into the net, only for Gomez to restore Wigan's advantage in stoppage time.
Stoke City defeated Fulham 1-0 at the Britannia Stadium, with Charlie Adam claiming the game's only goal in the 26th minute to take his side above Liverpool into 11th place.