Hector Bellerin had put Arsenal in front after latching onto a superb Alex Iwobi pass and beating Asmir Begovic, but two goals in four minutes turned the match on its head.
Callum Wilson converted a perfect Ryan Fraser cross in the 70th minute, before the striker turned provider, controlling a long ball and teeing up Ibe to fire past Petr Cech.
The victory moved AFC Bournemouth from 17th to 13th, four points above the drop zone. Arsenal remain sixth.
AFC Bournemouth: 20 Jan v West Ham (A)
Arsenal: 20 Jan v Crystal Palace (H)