Arsenal stuttered to a disappointing 0-0 draw at the London Stadium, though things could have been much worse when Javier Hernandez struck the crossbar late on.
Wenger handed a rare start to Wilshere and the England international looked sharp in midfield, dictating most of Arsenal's attacks.
For West Ham, the match ended a run of three difficult fixtures which saw them go up against Manchester City, Chelsea and the Gunners.
And although David Moyes expected the worst before them, he has been pleasantly surprised with the Hammers' performances, taking four points from those three matches.
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