Substitute Ryan Babel's second-half strike ended Manchester United's run of five successive league wins following the 2-1 result at Liverpool.
It also gave Anfield boss Rafael Benitez his first victory over the Old Trafford men in 10 Premier League attempts.
United took the lead early on through Carlos Tevez, but Liverpool forced their way back into the game with a bizarre Wes Brown own goal, before dominating the second period - which saw Nemanja Vidic sent off.
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