The deadlock was broken in the 19th minute with what was the first shot on target of note. The home team managed to work the ball wide on the left to Patrice Evra, who in turn drilled in a cross for Robin van Persie to beat Pepe Reina with an instant low shot from 10 yards out.
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Seven minutes later Van Persie had another chance to add to his tally, but he fired over the bar following a through-ball from Ashley Young.
As the half drew to a close Tom Cleverley saw his volleyed effort from the edge of the area flash just wide of the target. Then in stoppage time Martin Skrtel retreated to clear Van Persie's flick off the line.
Visiting Liverpool introduced new signing Daniel Sturridge into the action during the break and the England international's arrival resulted in the Merseysiders having a greater attacking threat.
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However, nine minutes after the restart United's advantage was doubled. Van Persie sent over a free kick to the back post for Evra, whose downward header bounced into the net via a deflection off his teammate Vidic.
Just three minutes later though Liverpool halved the deficit. A pass from Cleverley inside the United half was intercepted and Raheem Sterling in turn found Steven Gerrard. The Liverpool skipper's shot from 18 yards out was parried by David de Gea but substitute Sturridge was on hand to tap in the rebound from close range.
United responded positively and with 63 minutes gone Reina was forced to dive full stretch to his left in order to tip behind a curling effort by Shinji Kagawa.
Following that save, Liverpool then started to dominate the contest as they went in search of an equaliser.
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Italian replacement Fabio Borini, who had spent the last four months on the sidelines with a broken foot, sent a half-volley wide from 25 yards out which had De Gea scampering across his line.
Their best chance fell to Sturridge with six minutes on the clock. The hosts failed to clear their lines and the ball eventually dropped to the former Chelsea striker to the left of the target, but he only succeeded in sending the ball well over the bar.
It proved to be Liverpool's final clear opportunity as United held out to claim all three points, extending their lead at the top to 10 points in the process.