Robin van Persie's late penalty secured Manchester United's first Anfield win since December 2007 against ten-man Liverpool, on an emotional afternoon on Merseyside which ended 2-1 in the visitors' favour.
The hosts played 51 minutes with ten men after Jonjo Shelvey's sending-off but still managed to take the lead through Steven Gerrard's volley seconds after the interval.
However, Rafael equalised soon after and Van Persie, one of three United players to miss from the spot this term, scored his fourth goal in as many games against the Reds - although three of those had come for former side Arsenal - nine minutes from time.
The result left Liverpool rooted in the bottom three as their worst start to a campaign for a century continues, whereas United maintained their usual progress by moving up to second.
It was harsh on Brendan Rodgers' side, who continued to take the game to their rivals despite being short on numbers as they desperately looked for their first league victory of the season.
United may have left Anfield wondering how they managed to win, having hardly threatened in attack and failed to dominate midfield until the final quarter, but those concerns will have been of little consequence.
Once Ryan Giggs had flashed an early shot wide, the momentum was all with the hosts as a Luis Suarez cross-shot was stopped by Anders Lindegaard and headed away by Jonny Evans under pressure from Fabio Borini.
Shelvey sent off
Gerrard drove a low effort from Shelvey's corner into the side-netting and Suarez looped a right-footed shot wide before the match ignited. Shelvey robbed Giggs in midfield but as the ball broke free he launched himself at Evans and the inevitable outcome was a red card.
Even with a numerical disadvantage Liverpool continued to pressure United and Suarez drew Lindegaard into a low saw from his free-kick. The visitors would have been pleased to reach the interval with their goal intact but it took just 50 seconds after the restart for that to change.
Second-half substitute Suso, making his Premier League debut three days after his first-team bow, saw his cross half-cleared to Glen Johnson. A tackle from Paul Scholes, on for Nani at half-time, succeeded only in diverting the ball towards Gerrard, who volleyed home left-footed in front of the Kop.
It was short-lived, however, as within five minutes United were level when Shinji Kagawa laid the ball off for Rafael to brilliantly curl left-footed over Pepe Reina and in off the far post.
Penalty decides points
Rodgers' determination not to just shut up shop and settle for a draw was reflected in the approach of his team, who made light of the fact they were a man down, with Suso having a shot tipped over by Lindegaard and Suarez continuing to trouble the visitors' defence.
But as the match entered the final 20 minutes United began to take more control, although their winner came from their opponents giving away possession on the halfway line.
Daniel Agger and Johnson collided to allow Antonio Valencia to race 50 yards into the area and although Johnson got back he could only bring down the Ecuador international. Van Persie drilled home, although Reina went the right way and almost made the stop.
