The home side started brightly and broke the deadlock in the 14th minute thanks to Wayne Rooney. Ashley Young was brought down inside the area by Shaun Derry, who was handed a straight red card. Rooney stepped up to dispatch the resultant penalty past QPR goalkeeper Paddy Kenny.
United went on to create numerous chances during the remainder of the half, but Kenny was on hand to deny Rooney, while Young glanced a header wide of goal from close range.
The trend continued after the restart as United went about trying to make their numerical advantage count.
Danny Welbeck thought he had doubled United's lead in the 50th minute, but his strike was ruled out for offside.
Brazilian full-back Rafael then saw his effort pushed onto the bar by Kenny in the 58th minute, before the victory was sealed ten minutes later when Paul Scholes fired past the QPR goalie from 25 yards out.
Michael Carrick went closest to adding a third in the closing stages when his 30-yard drive struck the inside of the post.
United's lead will be cut to five points if Manchester City defeat Arsenal later today.