Eddie Howe's eye-catching Bournemouth side dominated the opening 25 minutes and should have been ahead with young Welsh striker David Brooks a thorn in the Everton defence.
Brooks struck a shot against the base of the post in the 14th minute after being played in by Junior Stanislas while Stanislas himself nearly embarrassed England keeper Jordan Pickford with a free kick.
Bournemouth also had two penalty shouts ignored before Everton gradually roused themselves, with defender Michael Keane heading against the crossbar shortly before halftime.
The hosts took the lead with only their second effort on target in the 61st minute. Lucas Digne did well to keep a ball in play and his hoisted cross was headed home powerfully by defender Zouma for his first Everton goal since joining on loan from Chelsea.
Everton's second in stoppage time, struck home excellently by Calvert-Lewin after great work by Ademola Lookman, was harsh on Bournemouth who will wonder how they went home unrewarded.
Bournemouth, who had 16 goal atempts, remained in 12th spot with 27 points from 22 games, nine points above the bottom three while Everton moved into 10th spot on 30 points. (Reporting by Martyn Herman Editing by Ian Chadband)
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