Ross Barkley had come in for some criticism earlier this season and there were some murmurs about him potentially leaving the club.
Everton are undefeated in their last six against bottom-six sides and have won five of their last eight against such teams by at least two - given how excellent they looked against Bournemouth recently, it wouldn't be a surprise to see them romp home again.
Sunderland started the second half brighter with Jermain Defoe unsuccessfully claiming handball against Ashley Williams when his volley struck the defender. "We are trying to achieve different things at the other end of the table, so there is a gulf in the quality of player".
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Moyes certainly didn't mince his words in regards to his aims for the weekend: "I want to go back to Everton and win".
While Sunderland continued to play tidily after going a goal down, they also continued to offer little in the way of a goal threat.
"You can take a bit of criticism from your manager now and then, but you have to react to it which I have done".
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Up to conceding the goal Sunderland had done a good job of restricting their hosts by making the game attritional and scrappy and Everton gradually succumbed.
The Blues' first goal was also the first for Gueye in the royal blue shirt. If it was not one of Lukaku's prettier goals, it was the type of opportunity few other forwards would have been able to accept. Lukaku showed speed, strength and determination in homing in on goal, as well as the ability to force the ball past Pickford.
In truth, Everton won without breaking sweat and Sunderland's relegration is looking increasingly inevitable.
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But although on paper, this will be one of their more easier assignments, a relegation threatened team is never easy to face, especially at this stage of the season.