With the game look dead set for a draw, Scholes popped up to score a free header beyond the diving Shay Given after he was left un-marked in the six-yard box.
Patrice Evra provided the cross from the left hand side after receiving the ball from Gabriel Obertan.
The win means that United kept the pressure on leaders Chelsea who will face Tottenham in a late kick-off today.
Chelsea now have a one point lead at the summit.
Earlier, Wayne Rooney gave Manchester United a boost by returning to the side starting line-up.
Rooney was left frustrated in the first half, however, after returning from an ankle injury.
The England striker should have made the breakthrough in the 41st minute but dragged his effort wide.