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The visitors lacked creativity going forward, with the pace of Gabriel Agbonlahor seeming to be the only way forward for Paul Lambert's side.
Agbonlhaor's trickery almost opened the scoring before the break but his deflected effort was well kept out by Mark Schwarzer.
Steve Sidwell had the chance to send Fulham into the break in the lead but the midfielder headed wide from close range following good work from Hugo Rodallega on the wing.
However, with six minutes remaining a free kick made its way to Baird and the defender finished smartly to earn the points for the Cottagers.