The Dutch forward scored the game winner in the 81st minute after winger Antonio Valencia went down in the box following what appeared to be minimal contact from a challenge by Glen Johnson.
Referee Mark Halsey appeared to have been put in a difficult position. Johnson had his hand Valencia's back, but it was unclear how much pressure it had on him.
Liverpool played 51 minutes with 10 men following Jonjo Shelvey's red card. The Reds found a way to take the lead as Steven Gerrard's volleyed a shot past Anders Lindegaard seconds after the second-half whistle. It was an excellent finish for the long-time Liverpool star.
United would even the match five minutes later, as Rafael delivered a curling left-footed shot from the right side. Former Red Devils right back Gary Neville quickly praised the shot on Sky Sports, describing the young Brazilian shot as "absolutley sensational."
Defender Jonny Evans appeared to have fouled Liverpool forward Luis Suarez in the box, but no call was made.
Liverpool took 14 shots with six on target, while Manchester United had eight shots with three on goal. Liverpool barely edged United in possession at 52 percent.