Yarmolenko turned in the area to fire the Hammers ahead early on.
Joshua King equalised from close range, but only after the decision to disallow his close-range goal for offside was overturned by VAR.
Callum Wilson scored in a fourth consecutive Premier League match to put the Cherries ahead.
Nathan Ake then had an effort ruled out for offside against Dominic Solanke.
Aaron Ramsdale denied Yarmolenko an equaliser but was powerless to stop Cresswell forcing home a shot from eight yards.
The point extends West Ham's unbeaten run to six matches and takes them up to third on 12 points ahead of Leicester City's meeting with Newcastle United on Sunday, while AFC Bournemouth drop to seventh on 11.
AFC Bournemouth: 6 Oct v Arsenal (A)
West Ham: 5 Oct v Crystal Palace (H)