Only two of the new arrivals, Lewis Holtby and William Kvist, were registered in time to feature against Saints, who spent much of the first half on the backfoot and had goalkeeper Artur Boruc to thank for keeping the score level.
Fulham were made to pay for those missed opportunities in the second period as Southampton ruthlessly exposed their soft underbelly, with Adam Lallana opening the scoring after 64 minutes with a superb strike across the face of goal.
Rickie Lambert netted his 100th league goal for Saints six minutes later, before the visitors' other England international, Jay Rodriguez, curled home exquisitely in front of the watching national team manager Roy Hodgson.
While Bent saw a handball appeal turned down at the other end, it was Southampton in control.
Lambert was left frustrated after he could not make the most of a hashed clearance, only to then turn provider for the opening goal.
Collecting the ball just inside the Fulham half, the England forward played a wonderfully-weighted ball for Lallana to impressively fire low past Stekelenburg.
The 64th minute goal extended Fulham's wait for a clean sheet to a ninth match - the longest run in the top division - and they almost conceded again soon after.
Only a late block saw a Steven Davis strike wide, before Lallana started a great counter-attack and fed the ball to the overlapping Shaw, whose low cross was prodded wide by Rodriguez.
Southampton did not have to wait long for another goal, though.
Nathaniel Clyne, on as a 58th-minute substitute for the injured Chambers, sent in a fine low ball from the right, which, thanks to an intelligent stepover by Rodriguez, fell perfectly for Lambert to slot home.
Rodriguez's selflessness was rewarded in the 75th minute with a goal of his own. Lambert's long ball to the forward was controlled by his fellow England international, who cut inside away from Hangeland and curled home brilliantly into the top right-hand corner.
Substitute Pajtim Kasami curled wide as Fulham looked to reduce the deficit in the closing stages, but they failed to threaten Boruc as Southampton won a league game at Fulham for the first time since October 1947.
More top news
Sunday evening's weather for the east of the region
Sunday evening's weather for the west of the region
Fifteen of the remaining little ships that helped evacuate the beaches of Dunkirk in WWII have gathered in Chatham