In an eventful contest at Anfield, Sir Alex Ferguson's outfit conceded early in the second half before levelling and then going ahead late after the Reds were reduced to ten men when Jonjo Shelvey was sent off in the 39th minute.
It was a questionable decision by referee Mark Hasley as the young midfielders challenge on Jonny Evans was strong, and to a certain extent reckless, but he did make a genuine attempt at the ball and the United defender was not in control of his own tackle.
Nevertheless, Halsey brandished the red to disadvantage Brendan Rodgers' team who fought courageously throughout only to come up short.
In the first match at Anfield since it became official that Liverpool supporters were absolved of blame for the Hillsborough tragedy, the home side managed to open the scoring early in the second half through their influential captain Steven Gerrard.
The Reds may have had one less player on the pitch but they soon had the entire city behind them in the 46th minute when Gerrard fired past Anders Lindegaard with a lovely left-footed volley after controlling Glen Johnson's chipped pass on his chest.
However, less than five minutes later the visitors were back on level terms when Rafael produced a stunning lofted finish with his left foot from the right side of the area from a fairly tight angle.
With just over ten minutes remaining, United took the lead when Robin van Persie scored from the penalty spot, despite Pepe Reina getting a hand to the shot, after Johnson had nudged Antonio Valencia just as he was about to pull the trigger. The midfielder had broken from inside his own half before advancing into the area and just as he was about to shoot, the Reds defender but enough of a touch on from behind to prompt referee Halsey to point to the spot.
Liverpool were the better team on the day and deserved more than what they got with Lindegaard the busier of the two goalkeepers but the weight of numbers and a slightly more efficient attacking display from United forced the result which allows last season's runners-up to move second on the table.
Unfortunately for the Reds, their winless streak was extended to five games as they sit 18th on the table on the back of their worst start in over 100 years.
Anfield, Liverpool - 44,263