Jamie Mackie put QPR ahead at Old Trafford, where Redknapp was watching from the stands hours after replacing the fired Mark Hughes.
But the west London team failed to secure its first win of the season, with Jonny Evans equalizing before Darren Fletcher and Javier Hernandez scored to put United back on the winning path after losing at Norwich last weekend.
United is now two points ahead of Manchester City, but the defending champions are at Chelsea on Sunday.
West Bromwich Albion dislodged Chelsea from third by winning 4-2 at Sunderland on Saturday.
United beats QPR, exposing task facing Redknapp
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