Scholes, Manchester-born and a product of the United youth system, steered home from close range in the 39th minute to mark a milestone match in the 31-year-old's United career.
England defender Rio Ferdinand scored a rare goal in the 66th minute, superbly bringing down a high ball with his right foot and then driving beyond keeper Jose Reina with his left.
Victory propelled United back to the top of the Premier League on goal difference ahead of champions Chelsea, who beat Portsmouth 2-1 at Stamford Bridge on Saturday.
Defeat for Liverpool all but killed off their hopes of mounting a title challenge. They are already 11 points adrift of the leaders and remain mired in mid-table.
They deserved no more than they got on Sunday, proving unable to upset a dominant United performance.
Scholes can only have dreamed of being on the scoresheet as he became the ninth United player to reach the 500-game milestone, joining team mates on the day Gary Neville and Ryan Giggs.
His team applied all the early pressure, but despite the enthusiasm of Louis Saha, who tried his luck with an angled shot, and strike partner Wayne Rooney, who just failed to get on the end a through-ball, there were no clearcut chances.
Liverpool carved out their best opportunity when Dutch forward Dirk Kuyt got in a header from Mark Gonzalez's cross from the left but the effort was easily saved by keeper Edwin van der Sar.
SLACK DEFENDING
United finally broke the deadlock thanks to some slack defending, which left Scholes completely unmarked on the edge of the six-yard box to receive Giggs's square ball from the left.
Reina managed to block Scholes's initial sidefoot shot but the United midfielder made sure by touching the ball over the line as Sami Hyypia tried to clear.
Minutes after Scholes's first league goal of the season, United were nearly 2-0 up when Saha unleashed a low shot from the edge of the area which Reina just tipped round the post.
At the other end, a rasping effort from Liverpool's Spanish midfielder Xabi Alonso in first half stoppage time underlined a latent threat from Rafael Benitez's men.
But United put the game beyond their reach soon after the re-start, when Giggs sent over a teasing cross, the injured Jamie Carragher failed to make a solid clearance and Ferdinand pounced.
It was the defender's first of the season, and only his fourth in more than four years with United.
The hosts then went on to control the game, albeit without threatening to add to their tally, while Benitez threw on striker Peter Crouch in a vain attempt to add bite to his attack.
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