With Bournemouth desperate to secure their first league victory in nearly a month, Artur Boruc started in goal ahead of Asmir Begovic while West Ham left unsettled striker Marko Arnautovic, who has been linked with a big-money move to China, out of their squad.
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.
The Chilean isn't convinced that his top goalscorer is in the right frame of mind to feature at the Vitality Stadium.
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.
West Ham have so far refused to accept any bids and urged Arnautovic to honour the contract he signed when joining the club from Stoke in 2017.
He told his post match press conference: "I am disappointed about the result".
But now reports are suggesting that West Ham have made a decision regarding Marko Arnautovic and the club will not be letting him move out this month.
"From our side we will have to be very concentrated, try not to allow them to score, and of course our team always tries to score".
He appeared to wave goodbye to supporters after being subbed in the 1-0 win over Arsenal at the London Stadium.
Pellegrini, though, does not expect Arnautovic to refuse to play for Saturday's (Jan 19) trip to Bournemouth. We played without Marko four or five games in December and we won those games.
The Hammers want to replace Arnautovic before letting him go and according to Sky Italia they are ready to make a move for Torino's Andrea Belotti.
"We will know what will happen about it in the coming days".
I don't think the Cherries have played especially badly in that time, which is one of the reasons I think they will return to winning ways on Saturday.