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The Saints have conceded fewer goals than any other team in England this season, just three in nine league matches. However, to simply label Mauricio Pochettino's side as a strong defensive unit would be hugely unfair.
Southampton then dropped a gear after the break, but they still had enough about them to control possession and see out the game with minimal fuss.
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It was almost 2-0 moments later as Rodriguez went on a jinking solo run into the area before being denied by the fingertips of Cottagers keeper Maarten Stekelenburg.
Full of confidence, Lambert then struck the post after cutting in from the left and unleashing a powerful low drive from 20 yards.
Lambert played a key role as Southampton doubled their lead just before half time. Adam Lallana stood up a cross to the England international, who nodded the ball across goal to the far post, where Rodriguez arrived just in time to place a brave header beyond Stekelenburg.
Southampton's dominance continued in the early stages after the break and they almost added a third goal in the opening seconds of the second half, but Lambert uncharacteristically fluffed his lines in the penalty area.
Rodriguez then went close with a spectacular bicycle kick, while at the other end Fulham failed to make any real impression on the hosts' recently-erected defensive brick wall.
At least the visiting supporters could see the funny side though, chanting "we've only had one shot" following a wayward effort from Steve Sidwell late on.