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QPR, being watched from the stands by Harry Redknapp who was named as their new manager on Saturday (local time), took the lead with a 52nd-minute Jamie Mackie tap-in, but were left reeling as quick goals from Jonny Evans, Darren Fletcher and Javier Hernandez gave United their sixth comeback win in the league this season.
Now without a win in 13 league matches, QPR stay nailed to the bottom with four points.
United moved on to 30 points, two clear of champions Manchester City (28) who can regain top spot if they win at Chelsea (24) on Sunday.
West Bromwich Albion moved on to 26 points and above Chelsea into third place - at least until Sunday's match at Stamford Bridge - when they won 4-2 at Sunderland for a fourth successive league win, giving them their best start to a season since 1953-54.
Everton were minutes away from beating Norwich City but had to settle for a 1-1 draw after a late Sebastian Bassong header cancelled out Steven Naismith's early opener for Everton.
Wigan Athletic beat Reading 3-2 with a hat-trick from Jordi Gomez and Stoke City beat Fulham 1-0 with a first-half goal from Charlie Adam.