Joshua King added a second to confirm victory in the 90th minute but it was Wilson's 54th-minute effort that proved decisive as Eddie Howe's side registered only their third league win since the end of October.
But West Ham's momentum was halted when Fraser burst down the left flank and sent the ball bouncing to the edge of the box where Wilson swung a hammer of a shot that bulged the net to the right of Fabianski, who stood rooted to the spot as it flashed past him.
Guangzhou Evergrande are said to have offered £35 million for the 29-year-old, matching a reported bid from Shanghai SIPG, the Chinese Super League champions.
Marko Arnautovic's move away from West Ham is now off.
However, Arnautovic's state of mind at missing out on £14.5million a year in wages could yet prove problematic and derail the club's season.
The club rejected a £35m bid for him this month and have made it clear that they will not be pushed into a selling him unless they can sign a replacement.
"If they agree, we don't have any problem to change".
"Marko has his head on another issue so it wasn't a good idea for him to play".
The Hammers travel to the Vitality Stadium to take on the Cherries on Saturday afternoon, though it remains to be seen whether Pellegrini will include Arnautovic in his matchday squad as he looks to push through a move.
That they are set to come together in China may indicate something about their motivation, but there can be no doubting their quality and what they did for the club during their time in east London.
Hammers boss Manuel Pellegrini admits the club is open to a deal and said: "They are not forcing me to sell Marko Arnautovic".
When asked about the absence of Arnautovic, Pellegrini said: "I never talk about one player when I lose a game because the team that played today couldn't win it".