The visitors started brightly, with David Brooks hitting a post from Junior Stanislas's pass after 14 minutes.
But Everton rallied, as Michael Keane climbed superbly to hit the crossbar with a header before half-time.
After the break, Nathan Ake cleared a Richarlison shot off the line, while Steve Cook went close with a header at the other end.
On 61 minutes Lucas Digne burst down Everton’s left and crossed in for Zouma to head in the opening goal, before Calvert-Lewin struck in stoppage time following good work from Ademola Lookman.
Everton climb to 10th, on 30 points, while AFC Bournemouth stay 12th on 27 points.
Everton: 19 Jan v Southampton (A)
AFC Bournemouth: 19 Jan v West Ham (H)