Premier League: Swansea 0 Southampton 1
The forward started the match on the bench, but bundled the ball over the line after a fluffed Ashley Williams clearance in the dying embers of the match to claim the three points in a fixture of little consequence at either end of the table.
A lack of significant incentives contributed to a low-key encounter at the Liberty Stadium, with clear-cut chances in scarce supply.
The visitors enjoyed the lion's share of possession, but failed to cause Swansea goalkeeper Michel Vorm too many problems for the best part, while Artur Boruc had a comfortable 90 minutes at the other end.
Wilfried Bony and Sam Gallagher each wasted great opportunities to break the deadlock – both sending efforts over the crossbar in the opening period.
But it was Lambert's scrappy effort at the death that settled matters.
The result means Southampton are assured of an eighth-place finish at the end of the season.
Lambert was among the substitutes after failing to shake off a gluteus muscle injury, and it was the visitors' rear guard that needed to be on high alert in the opening minutes.
Jonjo Shelvey squared the ball to Bony, who back-heeled to Pablo Hernandez, but goalkeeper Boruc denied the Spaniard before Jonathan de Guzman blazed over.
But the tempo of the match began to resemble that of a pre-season friendly or exhibition.
Dejan Lovren curled a 20-yard free-kick narrowly over the crossbar in 20th minute, before a Gallagher header from a dangerous Nathaniel Clyne cross suffered the same fate just past the half-hour mark.
Bony should have put Swansea in front soon after, but after collecting the ball from a Hernandez touch, the Ivorian powered his effort well over.
Southampton enjoyed the majority of possession in the opening period, but failed to make it count as the sides went in goalless at the interval.
Adam Lallana's 25-yard drive shortly after the break forced Vorm into his first real save of the encounter, while the biggest cheers from home supporters came as news of fierce rivals Cardiff City's slide towards relegation filtered through.
Goalscoring opportunities were at a premium for both sides, and Shelvey's low free-kick on the hour was too tame to trouble Boruc in the Southampton goal.
But Southampton had the final say, as Lambert put the ball in the back of the net to seal the visitors' first win at Swansea in the last eight attempts.