Jean Tigana's men should have won by a much greater margin at Craven Cottage, though, but for their profligacy in front of goal.
Last season's First Division champions, who have struggled with the transition to the top flight, wasted numerous opportunities against another side at the wrong end of the table.
Their lack of poise in the area could have cost them late on as Anders Svensson struck the crossbar for the visitors, who had levelled through James Beattie.
Gordon Strachan, who saw his new side throw away a two-goal lead twice in his first match in charge, a 3-3 draw with Ipswich in midweek, watched his team outplayed for the most part after a quiet start.
A third away victory in the league was never on the cards and Malbranque, a £4.5million summer signing who was recalled in place of Lee Clark, made sure Svensson's creativity down the right produced the first threat of the match but his third-minute centre following a dash down the right was negated by Luis Boa Morte, tracking back into his own area.
Fulham for their part enjoyed much of the early possession but when Steve Marlet's neat turn allowed him to run clear of the visitors' defence he was denied by a well-timed challenge from Claus Lundekvam.
Then, just before the quarter-hour, the record £11.5million signing escaped down the left only for his cross-shot to be repelled by Saints goalkeeper Paul Jones.
Southampton, who have won twice on the road in the Premiership so far this season, could have taken the lead in the 18th minute as the ball pinged about the Fulham box and Matt Oakley's shot bobbled wide.
But it was the home side who always looked likelier to score and they did so seven minutes later.
Barry Hayles, again preferred to Louis Saha up front, twisted and turned in the box, his shot was blocked by Jones' legs and with the goalkeeper floored,
Marlet headed goalwards for Malbranque to steer in from a couple of yards ahead of Jo Tessem.
Indecision in the Fulham backline allowed the visitors to restore parity, however, in the 32nd-minute.
Tahar El Khalej's header from inside his own half looked innocuous enough with Marian Pahars running back from an offside position.
But with the hosts' defence waiting for a whistle, James Beattie was allowed to proceed by referee Andy d'Urso and despite getting the ball stuck under his feet while advancing on Edwin van der Sar's goal, regained his composure to sidefoot past the advancing Dutchman.
But the scores remained level for just 60 seconds as Malbranque, who like Marlet gave up Champions League football with Lyon for west London, claimed his second of the afternoon and fourth of the season.
Steve Finnan's low cross was taken off Marlet's toes by El Khalej, the ball ran to Malbranque and he lifted into the roof of the net from eight yards.
Former Southampton winger Boa Morte, who had gone close just before the interval with a drive into the side netting, went on a jinking run across the area at the start of the second, helping the ball to Malbranque, whose cross was turned over by Hayles.
Saha, on as a half-time replacement for Marlet, should have done better when van der Sar's long ball forward sent him racing clear, lifting his effort way too high.
Fulham, whose Achilles heel this season has been scoring goals, continued to create chances and they were close to making it 3-1 through Boa Morte.
Hayles and Malbranque attempted to swap passes but the ball ran loose to the Portugal international, who curled a left-footed attempt against an upright and Saha flashed the rebound wide.
The latter's pace afforded him another opportunity moments later, though, this time seizing on a punt forward, beating the onrushing Jones with his lob, which drifted agonisingly wide.
Malbranque was denied a hat-trick 17 minutes from time as Jones spectacularly tipped his well-placed effort from the edge of the area around a post.
And the Wales number one excelled again by rushing out to smother at Saha's feet as the Cottagers' frustrations grew.
It could have been worse for Tigana's men in between those saves, however, as Svensson's speculative 30-yarder beat van der Sar and thudded off the crossbar for Pahars to somehow blaze over.
Then, substitute Dan Petrescu was left aghast at d'Urso's failure to spot Rufus Brevett charging down a shot with his hands in the box.
With the home crowd tense, there could have been additions to the score at either end but Boa Morte sent a shot wide and Pahars stabbed another off target at the other end.