In the third minute of stoppage-time, with the match petering out, Swansea captain Ashley Williams looped a clearance over Michel Vorm, off the crossbar and into the net, off the back of Lambert.
The ball may have already crossed the line, but will be one for the dubious goals panel.
In a game of few chances, Southampton enjoyed the lion’s share of possession without creating a great deal, while Swansea, especially after the break, were poor in the final third.
Wilfried Bony had the best chance of the opening period, firing over after latching on to a Pablo Hernandez flick.
Southampton enjoyed much freedom down the flanks, with full-backs Luke Shaw and Nathaniel Clyne getting in behind regularly, but they failed to really test Vorm in the Swansea goal.
Southampton are guaranteed an eighth-place finish already, while Swansea failed to make it three wins in a row, but will not be too concerned with safety already assured.
The first half was dominated by Southampton, who had 64 per cent of the possession, but it was the home side who had the best chances.
Wilfried Bony, whose recent desire to seek a move away from the Liberty Stadium won’t have sat well, looked a threat, and provided a real outlet.
Bony turned provider for the first real opportunity of the game, flicking into the path of Pablo Hernandez, whose tame effort was palmed clear by Saints stopper Artur Boruc, and Jonathan de Guzman fired the rebound over the top.
Southampton soon settled into their impressive passing rhythm, with Steven Davis key to their maintaining of the ball, and Schneiderlin should have done better than send a close-range header high over the Swansea bar.
However, apart from a Dejan Lovren free-kick that dipped over, clear-cut attacking opportunities remained few and far between.
Sam Gallagher wasted Southampton’s best chance when his 33rd-minute header failed to find the target.
Saints skipper Adam Lallana tested Swansea keeper Michel Vorm with an angled shot as the second period began, while Swansea continued to rely on the bustling Bony for any realistic threat on Southampton’s goal.
Jose Fonte was then cautioned for a foul on Hernandez, but Swansea tamefully wasted the opportunity with still no sign of Boruc or Vorm being seriously troubled.
Swansea were guilty of giving possession away far too easily in midfield and Lambert joined the action 30 minutes from time when he replaced Lallana to give Saints renewed attacking impetus.
Nathan Dyer followed Lambert off the bench as Swansea’s first substitute, taking over from De Guzman, and there was certainly more urgency about the home side as they looked to secure a third successive league win following victories over Villa and Newcastle.
It was not to be, and Lambert, via his back, snatched all three points as Southampton continued their impressive season.