The Foxes were promotion favourites at the start of the season after making several acquisitions but it was Southampton who led the pack going into the game having won their first four matches.
That made for an entertaining afternoon in the East Midlands, with the hosts finding themselves 2-0 up in the early stages through goals from Darius Vassell and Richie Wellens.
Dan Harding pulled a goal back for Saints before the defining moment came just before the break when Lambert headed past his own goalkeeper.
The goal was given, much to the visitors' dismay, despite Sol Bamba appearing to push the Saints striker.
David Connolly then pulled another goal back for Nigel Adkins' men after the break but it proved in vain as Leicester claimed the points.
Foxes manager Sven-Goran Eriksson made 10 changes to the side that overcame Bury in the Carling Cup in midweek, with Matt Mills the only player to keep his place in the XI.
The alterations had the desired effect in the opening stages, though, as they flew out of the blocks to take a third-minute lead.
Andy King was the orchestrator, capitalising on being afforded too much space to send in a delicious centre, which Vassell nudged past Kelvin Davis and into the net.
They could have been two soon after as Mills rose highest to meet Neil Danns' corner, only to be denied by an excellent Davis save.
They did grab a well-deserved second midway through the first period courtesy of a moment of real quality.
Jeffery Schlupp, looking a constant threat after replacing the injured David Nugent, held the ball up brilliantly before teeing up Wellens, who struck a gorgeous curler off the inside of the post from 25 yards.
It seemed to be all one-way traffic at that stage but Harding was on hand to drag Saints back into the game, nodding Adam Lallana's cross home.
The visitors were hit with a sucker punch on the stroke of half-time, though, as Lambert headed past his own goalkeeper under pressure.
There was certainly an air of contentiousness about it as the striker appeared to be pushed by Sol Bamba, with referee Scott Mathieson surrounded by angry Southampton players as he headed back down the tunnel at the break.
Clearly spurred on by feeling aggrieved, Saints came out strongly after the interval and after going close himself, Lallana crossed for Connolly to nod home.
The game entered a lull thereafter as both sides struggled to maintain the endeavour of the opening 60 minutes.
Leicester were left thanking goalkeeper Kasper Schmeichel in the dying moments as he brilliantly denied Lambert, looking to atone for his error, with a fantastic point-blank save.
Lallana also spurned another chance soon after as Leicester held on to claim the three points.