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The Irish winger nearly doubled the Cottagers' lead, but his shot went just wide of Jussi Jaaskelainen's post.
Fulham went in leading at the break, but the Hammers were back on level terms three minutes after the break.
West Ham captain Nolan continued to terrorise the Fulham defence but was unable to find a way through a stubborn backline.
Mladen Petric could have sealed the points with 10 minutes remaining, but Jaaskelainen was equal to his effort.
Joey O'Brien's own goal in the last minute saved the Craven Cottage faithful from a nervy final few moments.