After a goalless first period in which Darren Bent had forced Artur Boruc into three good saves, Lambert found Lallana who slotted home the opener on 64 minutes from the left side of the box.
The unmarked Lambert doubled the advantage six minutes later – scoring his 100th league goal for Saints – after being found by substitute Nathaniel Clyne in the box.
The visitors’ other England international, Jay Rodriguez, made sure of the win with the third on 75 minutes with a fantastic finish after cutting in from the left following a long-range pass from Lambert.
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.
Only two of the new arrivals, Lewis Holtby and William Kvist, were registered in time to feature against Saints but there was no immediate reaction as Rene Meulensteen’s side crashed to another defeat at home.
However, 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 before Brede Hangeland met another fine Holtby corner with a header in the 24th minute, which brought an expert one-handed save from Boruc.
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 Maarten Stekelenburg before Bent was thwarted twice in a matter of minutes by Boruc, who first got down brilliantly to prevent the on-loan striker from rifling home after neat interplay.
Bent was then put through after Wanyama was dispossessed, 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 saw Rodriguez shoot wide, Schneiderlin’s audacious overhead kick fly over and Stekelenburg denying a Lallana strike from distance.
While Bent saw a handball appeal turned down at the other end, it was Southampton in control.
The visitors took the lead on 64 minutes when Lambert, collecting the ball just inside the Fulham half, played a wonderfully-weighted pass for Lallana to impressively fire low past Stekelenburg.
The goal extended Fulham’s wait for a clean sheet to a ninth match and they conceded again soon after.
Clyne, on as a 58th-minute substitute for the injured Calum Chambers, sent in a fine low ball from the right, which, thanks to an intelligent step-over 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 was controlled by his fellow international, who cut inside away from Hangeland and curled home brilliantly into the top right-hand corner with the England manager Roy Hodgson watching from the stands.
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 Craven Cottage for the first time since October 1947.