The Saints dominated possession in the opening minutes, but struggled to create a decent chance.
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Fulham then saw Dan Burn's header drop onto the roof of the net, before Steve Sidwell almost sliced an inswinging cross into his own goal, but Maarten Stekelenburg parried the bobbling ball away to safety.
The home side were a threat, however, particularly down the right, from where Sascha Riether was able to put in teasing crosses.
Scott Parker and Sidwell then dragged their efforts wide of the post, before the home players and fans appealed for a penalty when the ball hit the arm of Maya Yoshida. However, the referee waved away the appeals.
The Southampton goalkeeper then made two fantastic saves. Darren Bent latched onto a Parker pass and saw his volley tipped away, but the ball came straight back and the striker hit a low effort at Boruc.