Lambert's clinical volley was enough to earn the points for Saints, but that only told a fraction of the story on a thrilling night in West Yorkshire.
Lambert's strike was one of only two meaningful efforts the Saints had all game, while at the other end Leeds twice hit the woodwork, twice missed open goals, had a strong penalty claim turned down and were denied on several occasions by the brilliance of goalkeeper Kelvin Davies.
He continually repelled all that was thrown at him, with Luciano Becchio and Danny Webber particularly unlucky, while Becchio and Darren O'Dea also hit the bar as Leeds, invigorated by the arrival of veteran boss Neil Warnock, threw everything they could at their opponents in a bid to keep their own promotion dream alive.
But, while Southampton are now four points clear, Leeds are six points shy of the play-off places and Warnock may have taken over too late to mastermind a late rally. It is likely, though, that both managers will have left happy although for differing reasons.
The tone for what was to come was set in the fourth minute when Robert Snodgrass had a penalty appeal turned down when his shot hit the arm of Jose Fonte, while Davis smothered an Adam Clayton volley.
Leeds continued to press and only a smart block from Jos Hooiveld prevented Ross McCormack from getting a two-yard strike in before, entirely against the run of play, Southampton opened the scoring.
When Jack Cork picked the ball up with 16 minutes gone, it was the first time Saints had enjoyed possession in Leeds' half, but it did not show as his cross was knocked down by Tadanari Lee into the path of Lambert, who smashed a vicious volley beyond Andy Lonergan.
It was Lambert's 24th goal of the season and arguably his most emphatic but, as soon as the game restarted, Leeds were back on top.
As if the goal had not happened both Snodgrass and McCormack saw volleys skim over and wide, before the latter's header from the former's low cross was brilliantly kept out by Davis.
Then, six minutes before the break, Snodgrass fashioned Leeds' best chance which should have brought an equaliser. He worked Richardson again and his curling cross needed nothing more than a touch - something Aidy White somehow failed to do.
The barrage continued into the second half with Becchio putting a Snodgrass cross over and Clayton having a drive blocked by Hooiveld.
Southampton won their first corner in the 51st minute but remained firmly on the back foot, although Adkins was unhappy that Michael Brown went unpunished after an aerial collision with Cork.
If Adkins was unhappy with Miller then he will have been delighted with Davis, who continued to repel Leeds with a stunning trio of saves inside five minutes.
First, after failing to gather a cross he scrambled back to claw a Becchio effort off the line, then he twice made himself big to deny Leeds debutant Webber. The former Portsmouth striker had only been on the pitch a matter of seconds when his six-yard drive was tipped over, before he then saw a low effort turned away.
Becchio should then have done better after bringing the ball down in the box and McCormack was off target with a header, while Davis got out to Webber to force him to stab wide when a goal looked on the cards.
Southampton were clinging on for the final whistle now and, when Becchio and O'Dea both headed against the bar and Tom Lees had a stinging shot blocked in amongst a late melee, it was clear that it was going to be their day.