After a tepid first half, Saints took total control of the second period and destroyed Fulham with three goals in 11 minutes at Craven Cottage.
Lallana started the spree with a fine finish to celebrate his 250th Saints appearance.
Lambert added the second, his milestone 100th league goal for the club, before Rodriguez bent a fine effort into the top corner to seal a resounding and thoroughly deserved victory in front of the England manager.
The renewed optimism brought by Fulham's late flurry of transfer activity quickly evaporated as Southampton became the eighth side to take three points at Craven Cottage this season.
Staring down the barrel of relegation, the Whites took drastic action in a bid to retain their Premier League status by undergoing a 48-hour rebuilding project.
Six players arrived and four players departed Craven Cottage in that period, although there was no immediate reaction as Rene Meulensteen's side crashed to a 3-0 defeat at home to Southampton.
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.
Few would have expected such a rout after a confident first-half display from Fulham.
Their first chance of note came after eight minutes when Dan Burn met a Holtby corner with a towering header, which flew just over.
Scott Parker and Steve Sidwell fluffed efforts from distance as Meulensteen's side looked for the breakthrough, while Parker also saw a penalty shout for handball against Maya Yoshida waved away.
Other than a deflected cross that Maarten Stekelenburg fumbled, Southampton were creating little and would have gone behind in the 24th minute was it not for an expert one-handed save from Boruc.
Brede Hangeland met another fine Holtby corner with a header, which was somehow clawed away by the back-tracking Poland goalkeeper.
Southampton were not looking their free-flowing usual selves, with the defence looking unsteady and Victor Wanyama just ahead of them looking rusty on his return from almost two months on the sidelines.
The powerful Kenyan was misplacing many passes and was booked just 26 minutes into his return for clattering Parker, joining team-mate Rodriguez in referee Mike Jones' notebook.
Morgan Schneiderlin saw a header pushed around the post by Stekelenburg on a rare voyage forward by the visitors, who were again relying on their goalkeeper to keep the scores level.
Darren Bent was thwarted twice in a matter of minutes by Boruc, who first got down brilliantly to deny the on-loan striker rifling home after neat interplay.
The former England international was then put through after Wanyama was dispossessed and left in a heap, although the Southampton goalkeeper was again a match for him.
Schneiderlin became the third Southampton player booked as the break approached, with Rodriguez heading wide before the half-time whistle went.
Unsurprisingly, Wanyama was replaced by Jack Cork for a second half which began with the ball being worked out to the right, where Rodriguez fizzed an effort wide.
Schneiderlin saw an audacious overhead kick fly over, before Stekelenburg denied a Lallana strike from distance.
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.