This victory was just Everton’s second win in nine league matches and the first time they had kept a clean sheet at their Goodison Park ground since November 24.
The deadlock in an often frustrating match was eventually broken when, with Everton having had just one shot on target and south coast visitors Bournemouth a mere two, Zouma — on loan from Chelsea — scored his first goal for Everton in the 61st minute.
An Everton setpiece was cleared by the Cherries’ defence before Lucas Digne kept the ball alive on the left.
His flighted cross left Nathan Ake kicking at fresh air and, with goalkeeper Asmir Begovic not coming to collect, the onrushing Zouma leapt to power in a header that delighted the home crowd.
It was the 24-year-old French centre-back’s first goal since he scored for Stoke in a 2-2 draw with Brighton in November 2017.
A nervous Everton then had to survive concerted Bournemouth pressure at the end of a rainswept encounter before, in the fifth minute of stoppage time, the Toffees put the result beyond doubt.
Ademola Lookman did well to win the ball back and then, rather than just run it into the corner, he had the awareness to lay it back into the path of Calvert-Lewin, who had only been introduced into the action by Everton manager Marco Silva in the 87th minute.
Calvert-Lewin, who had replaced Richarlison, still had work to do but his low strike from some 16 yards out arrowed into the corner of Begovic’s net.
It was an excellent piece of build-up play from Lookman, with the forward making just his second league start of the season in a match where defender Nathaniel Clyne, on-loan from Everton’s local rivals Liverpool, was making his Bournemouth debut.
Despite their ninth defeat in 12 league matches, Bournemouth remained in mid-table safety and the result might have been different for Eddie Howe’s men if David Brooks’s shot had not rebounded clear off a post in the 18th minute.
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