Manchester United bounced back in style from their chastening defeat by Arsenal by cruising to a 3-0 victory over Everton at Goodison Park. After a 3-0 loss to Arsenal before the international break, United manager Louis van Gaal challenged his players to respond like champions. And, while not a vintage performance, at a venue where they have come out on the losing end in the last three seasons, quick-fire first-half goals from Morgan Schneiderlin and Ander Herrera followed by a second-half strike from Wayne Rooney against his former club delivered a welcome three points.

The result keeps United just two points behind Premier League leaders Manchester City, and, for the time being, sees them move three points ahead of Arsenal, who visit Watford later on Saturday. In truth, they didn’t have to do an awful lot to get control of the fixture.

Everton had lost just once in 10 matches in all competitions this season, yet it was they who made a surprisingly sluggish start and throughout contributed heavily to their own downfall. Defensive lapses allowed first Schneiderlin to confidently side-foot home in the 18th minute to net his first goal for Manchester United after Everton failed to clear a corner. Just four minutes later, Marcos Rojo was given free rein of the left flank and delivered a fine cross that an unchecked Herrera headed down and past Tim Howard.

Herrera’s inclusion in the team was one of the major plusses for United. And the Spaniard played a big part in United effectively sealing victory just past the hour mark. Again Everton were culpable, this time the man who captained England during the week, Phil Jagielka, gave the ball away and then, after Herrera’s through ball, watched on as England’s record goalscorer easily beat Howard. While some of the hostility once felt between the Everton crowd and their former idol has now dissipated, there was still evident delight on Rooney’s face in getting just his second Premier League goal of the season.

Rooney was moved back into his favored central striker role for the fixture, with Anthony Martial, despite his impressive start to his United career up front, being shifted out to the left. It meant Memphis Depay was one of the main casualties of the Arsenal defeat, watching on from the bench, along with Netherlands teammate Daley Blind. In the versatile Dutchman’s place, Phil Jones made his first start of the season.

Certainly there was a more solid look about Van Gaal’s side than when being torn apart by Arsenal. And that was helped, too, by Morgan Schneiderlin’s return to the midfield. The France international is not in the side to get goals, but he showed impressive composure to get off the mark for the club he joined from Southampton in the summer and set them on the road to victory.

Steven Naismith could only half-clear a corner as he appealed that he had been unfairly eased away from the ball by Rooney. With play going on, Rojo helped the ball back into the penalty area and Chris Smalling chested wide for Schneiderlin to take his chance first time.

Two more of the players returning to the side soon combined to double United’s lead. Rojo, impressive defensively in a left-back slot that has been a concern for United since Luke Shaw’s serious injury, also produced going forward to set up Herrera to get his second goal of the season.

It could have been more before the interval, if not for Martial failing to seize an opportunity from Rooney’s cut back. But Everton began the second period displaying some of the purpose that was so missing from their performance in the first. Indeed it took a typically superb save from David de Gea with an outstretched left leg to stop Romelu Lukaku from getting Everton back into the fixture.

But any momentum Everton were building up was then decisively undone by further sloppiness. Jagielka gave possession straight to Schneiderlin, who quickly found Herrera on the right. From there Everton could not recover and Rooney had little trouble beating Howard. On a woeful day for Everton, the scoreline could have been made even worse late on, but United will be more than happy with as comfortable a victory as they may get all season.