Marc Pugh cancelled out Tom Cleverley's goal two minutes after the Everton midfielder opened the scoring in the first half, but it was Leighton Baines's 64th-minute strike that gave the Toffees all three points.
The result may give manager Roberto Martinez some breathing room, but a large number of the supporters are intent on the Spaniard leaving the club.
Discover how the game unfolded in Sports Mole's text commentary below.
Subs: Robles, Hibbert, Oviedo, Lukaku, Mirallas, Osman, Hassan
Subs: Gosling, Stanislas, Afobe, Federici, Grabban, Wiggins, O'Kane
The man himself, though, is not backing down. Earlier this week he told reporters: "Scrutiny I welcome and accept. I understand it completely. But it shouldn't be scrutiny of the last two or three months. It should be of three seasons, scrutiny about the team we've put together.
"The first season we had a record points tally, last season we were the last team in the British game to be knocked out of Europe, this season we made two semi-finals.
"I'm ready to fight more than ever to find a way to challenge for silverware."
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In response, he told reporters: "I don't think I have to reaffirm my commitment here every week, which seems to be a regular pattern. I love it here and I'm committed to the job.
"When you're a manager yourself you have the full support and understanding of other managers. It's a very difficult profession and you're judged constantly every week on your results, on a lot of aspects of your job. It's very tough at this level."
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