Wayne Rooney gave the visitors the lead when curled in from 25 yards in the 16th minute – despite appearing to be offside in the build-up – before George Thorne equalised before half-time.
Daley Blind then turned home Jesse Lingard’s cross in the 65th minute before Juan Mata sealed victory seven minutes from time to relieve some of the pressure on manager Louis van Gaal.
Speaking on BBC Sport after the final whistle, former United goalkeeper Schmeichel said: “In the second half, I’m not going to say it was brilliant, but it was so much better than what we’ve seen in recent weeks.
“It was much better than the first half and the big positives today were the full-backs. When I see Varela play, I don’t understand why he’s been on the bench. He was superb.
“I think the performance in the second half was really good and as a fan I was really happy with what the team did.”
United have been struggling to find consistent form in recent weeks and endured a winless December, before losing to Southampton in the Premier League last weekend.
The Red Devils have only won two of their last 10 Premier League games and are currently five points adrift of the top four.
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