It was United who started the better and Ryan Giggs just struck an effort wide of the target with six minutes on the clock. Liverpool had a glorious chance moments later when Luis Suarez drilled a low cross into the box, but Anders Lindegaard palmed the ball to safety.
The home side continued to create chances in the early stages, but Steven Gerrard's strike just moved wide of the post as both sides exchanged possession in a frantic opening.
Liverpool continued to dominate in the latter stages of the half, but they could not force an opening. They were reduced to 10 men late in the half when Jonjo Shelvey was dismissed for a high challenge on Jonny Evans.
The home side took the lead moments into the second period when Gerrard smashed an effort home from the edge of the area. However, United were level moments later when Rafael bent an effort into the top corner.
Both sides had chances to take the lead as the match approached the hour mark, and it remained end-to-end as both managers made changes. United forced a penalty after 77 minutes, however, when Glen Johnson felled Antonio Valencia in the area, with Van Persie stepping up to send United ahead.
Liverpool nearly levelled after 83 minutes when Martin Kelly met a Suarez cross, but he just headed wide of the target. Both sides picked up injuries in the latter stages, but it remained 2-1 to the away side.