Robin van Persie scored a late winner from the penalty spot as Manchester United overturned a one-goal deficit against 10-man Liverpool at Anfield.
Liverpool dominated the first half, but Jonjo Shelvey was sent off before the break after a dangerous lunge at Jonny Evans.
Steven Gerrard, however, put the home side ahead shortly after the interval when he steered home following a mistake from Paul Scholes, while Rafael levelled with a delightful finish.
Liverpool continued to carve out chances despite their numerical disadvantage, but it was United who claimed a winner after Van Persie converted following a foul by Glen Johnson on Antonio Valencia.
After a week or so of drama and discussion off the field, it was a relief to both clubs to see hands shaken and Hillsborough respected prior to the kick-off.
Liverpool showed no hangover from the momentous findings of the Hillsborough independent panel, starting the encounter with far more energy and dynamism than their great rivals.
A half-time lead would not have been undeserved for Brendan Rodgers' side, but they entered into the break level and a man down.
Shelvey was shown a straight red after he dived into a 50/50 challenge with Evans, who also appeared to fly recklessly into the tackle.
Liverpool, though, were ahead just a minute after the interval when Gerrard controlled an interception from Scholes and expertly half-volleyed past Anders Lindergaard.
Rafael pegged the home side back five minutes later with a spectacular finish, curling deliciously past Pepe Reina's outstretched hand and in off the Spaniard's far post.
The comeback was complete with only nine minutes remaining when Van Persie converted from the penalty kick - his fifth goal for Manchester United since joining from Arsenal.
Liverpool are still without a win in the Premier League this season, while Manchester United climb to second - one point behind leaders Chelsea.