Bolton did not have long to wait for a second goal when, six minutes later, Davies crossed to Cohen, who headed the ball back for midfielder Jack Wilshere, on loan from Arsenal, to volley in his first Bolton goal.
Alessando Diamanti ensured a nervous finish for the Lancashire side, however, when he pulled a goal back for West Ham two minutes from time and the Irons just missed out on a point when Junior Stanislas hit the crossbar.
Victory left the Trotters five points above the bottom three.
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