The Trotters opened the scoring in the 10th minute, Chung-Yong Lee sending in a pinpoint cross towards Davies who powered his header past Robert Green.
West Ham were shell-shocked and Bolton’s lead was doubled six minutes later, Davies exploited some hesitant defending and hooked the ball towards Tamir Cohen who nudged it into the path of Wilshere, the youngster made no mistake for his first goal of the season.
Carlton Cole looked certain to pull one back for the Hammers when through on goal but Sam Ricketts denied the England hopeful with a fine tackle and Johan Elmander missed a great chance for the visitors just before half-time.
Bolton were reduced to 10 men with around 20 minutes remaining when Cohen received his second yellow card for a foul on Scott Parker but they stood firm until the 88th minute when Alessandro Diamanti pulled one back with a fabulous strike into the far corner. Davies and substitute Junior Stanislas both hit the woodwork in a frantic five minutes of added time but Bolton hung on to ease their relegation worries.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.