Rooney, who went back to his boyhood club in July after 13 years with United in which time he scored a club-record 253 goals, wasted two good chances to cancel out Antonio Valencia's stunning early strike for the hosts.
He was substituted late on and then watched United add three more goals through Henrikh Mkhitaryan, former Everton striker Romelu Lukaku and Anthony Martial.
A rather flattering victory lifted United level at the top with Manchester City. Both sides have 13 points from five games and have scored and conceded the same amount of goals.
Everton, who had dominated much of the second half despite having little recovery time from Thursday's Europa League defeat by Atalanta, dropped into the bottom three with four points.
"I think the performance was very good, especially in the first 30 to 35 minutes," United manager Jose Mourinho said. "It was probably our best performance of the season.
"There was a moment were I felt we did not kill it so we have to make it solid with Ander Herrera. The second goal went in, then game over."
Everton manager Ronald Koeman said his side's third heavy defeat in eight days was undeserved.
"Sometimes in football you get more than you deserve but today we deserved more than we got," he said. "What I saw today of my team made me happy."
United took the lead after three minutes with a goal of stunning quality.
Nemanja Matic played a crossfield pass and as the ball zipped off a rain-soaked surface, Valencia connected with a right-foot shot that flew past Jordan Pickford into the net.
Rooney was given a warm ovation before kick off from the United fans, some of whom held up banners saying "Red Legend", but it was not a memorable afternoon for the 31-year-old former England skipper.
After 20 minutes he slid a left-foot shot wide of the post and in the second half he shot straight at United keeper David de Gea from close range, while Gylfi Sigurdsson was also denied by the Spaniard.
Juan Mata struck the post for United with a left-foot free kick before Lukaku, who wasted a good chance in the first half, set up Mkhitaryan after 83 minutes to slide in United's second -- the move stemming from a mistake by Ashley Williams.
Lukuku joyfully rammed home his fifth league goal of the season as the game moved into stoppage time before former United player Morgan Schneiderlin handled in the area and substitute Martial tucked away the penalty.
(Reporting by Martyn Herman; Editing by Christian Radnedge)
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