Both sides made five changes from last time out, with the hosts having to cope without injured midfielder Paul Pogba, who was replaced by Marouane Fellaini, while there was also a recall for Marcus Rashford.
The Toffees welcomed back Jordan Pickford in goal, with Maarten Stekelenburg dropping to the bench.
The hosts were in front within four minutes as Nemanja Matic curled a pass across the Toffees penalty area and Antonio Valencia arrived on the right to lash home a superb first-time right-foot shot past a helpless Pickford.
United, buoyed by that early strike, dominated the play for large parts, with the visitors finding it difficult to break out of their own half.
Twenty minutes in Rooney, on his return to Old Trafford, shot wide from 20 yards out as the Merseysiders were finally able to push forward.
Six minutes later a defensive error allowed Romelu Lukaku a clear run on goal against his former club, but the big-money United recruit somehow missed the target from 15 yards.
Lukaku was denied again eight minutes before the break, as United ended the half on top.
However, Everton almost drew level within two minutes of the restart as David de Gea spread himself well to deny former Red Devils great Rooney.
The visitors then started to enjoy a greater share of possession that they had previously, but they were still struggling to carve put any meaningful openings.
They did so shortly after United made their first change, with De Gea again standing strong to deny Gylfi Sigurdsson.
At the other end Juan Mata saw a free-kick curl around the wall only to strike an upright, before sub Jesse Lingard fired over when well placed.
The hosts finally made the game safe five minutes from time as Lukaku picked up a loose ball and fed Henrikh Mkhitaryan, who finished coolly past the advancing Pickford.
Lukaku added gloss to the scoreline as he sidefooted home from close range after his own free-kick had been blocked by the defensive wall.
And there was still time for Anthony Martial to add a fourth goal from the penalty spot after Morgan Schneiderlin had been penalised for handball.