Davies' powerful header put Bolton ahead before 18-year-old Wilshere became the youngest scorer in the Barclays Premier League this season.
West Ham mounted a spirited comeback after Bolton had Tamir Cohen sent off in the second half and Alessandro Diamanti curled in a late consolation.
Both sides hit the bar in a frantic finale but Bolton held on for a sixth straight victory over West Ham - and their third this season - which takes them above the Hammers in the table.
Source: PA
Source: PA