Both sides made quick starts to the match, and it was West Ham who had the ball in the net first, only for Winston Reid's header from a corner to be chalked off by the referee for a push on Tommy Elphick.
Wilson then made it 2-0 to the visitors on 28 minutes as the striker latched onto a poor backpass by Cresswell to score from close range, before the striker spurned a chance for a quick hattrick as his shot from the right hit the side netting.
Bournemouth came close to a third goal through Charlie Daniels, but his shot from long range went wide, before Max Gradel forced a save from Randolph on the stroke of half time.
With the words of Slaven Bilic still in the minds of West Ham's players, the hosts made a quick start to the second half, and soon found a goal. Mark Noble was tripped by Josh King inside the penalty box, and the midfielder scored from the resulting penalty.
Substitute Marc Pugh came close to restoring the lead for the Cherries, but his shot was well saved by Randolph.
Pugh was not to be denied on 66 minutes though, as the winger surged past Carl Jenkinson before producing a cool finish.
West Ham were reduced to ten men on 79 minutes when Jenkinson was sent off for bringing down Gradel in the penalty area. Wilson scored the resultant penalty and the Cherries appeared to be out of sight.
But the Hammers pulled back another goal soon after, as Modibo Maiga dribbled past two men before producing a finish to score his first goal of the season.
West Ham came close to levelling the match again before the final whistle, but the Bournemouth defence was able to clear a goal-mouth scramble from a corner as the Cherries secured their first Premier League win.