Stoke did their best to ruin David Moyes' seventh anniversary as Everton boss but remain up to their necks in relegation trouble following a 3-1 defeat at Goodison Park.
Everton cruised into a two-goal first-half lead through Jo and Joleon Lescott, but did their best to throw away victory after the break.
Stoke pulled one back through Ryan Shawcross and continually threatened to steal a point, but they are still without an away league win this term after Marouane Fellaini hit a third in injury-time.
Everton opened with a flurry of chances, created with pace and movement that worried Stoke's big defenders.
Only a fine saving challenge from Salif Diao stopped Steven Pienaar finishing off a Fellaini cross, the Belgian now sporting a surprisingly cropped hair-cut. Leon Osman then fired over under pressure following Leighton Baines' cross.
Stoke produced some difficult moments via Rory Delap's long throws, but after 18 minutes Everton were ahead.
Fellaini lifted a neat ball into the box and Jo evaded Shawcross' challenge to hit a low shot that Thomas Sorensen only half stopped, the ball dribbling over the line.
Stoke seemed visibly deflated, and after 24 minutes it got worse when Lescott side-footed home after Sorensen was only able to palm out a Tim Cahill header following Osman's cross.
But Stoke, who recovered from 2-0 down at Aston Villa recently to grab a point, looked to again be embarking on similar powers of recovery when Shawcross headed home from Liam Lawrence's corner after 53 minutes.
But in injury-time Everton sealed the points when Fellaini brought down a Baines long ball and guided his shot past Sorensen.
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