Going into the game on the back of a first home defeat in more than a year - a 1-0 loss to Bristol City - Saints were desperate to get back to winning ways with Middlesbrough and West Ham breathing down their necks.
They looked on course to do that early on in the encounter but, after dominating the first half, were dealt a bitter blow when Lambert saw red in the 51st minute.
That proved the game's turning point as youngster Jake Forster-Caskey put Brighton ahead 15 minutes later, slotting home after Kelvin Davis denied Kazenga LuaLua.
Matt Sparrow wrapped up the points with a fine double, firing home a sensational 35-yard strike before adding another emphatic finish to ensure Gus Poyet's side's four-match losing run was brought to an end.
Boro's loss at Blackpool ensured Saints remained top, albeit on the same points as West Ham, who beat Coventry 1-0.
Despite heading into the clash on the back of a disappointing result last time out, Saints enjoyed the better of the opening exchanges as they dominated proceedings.
They almost took an early lead when Adam Lallana's effort was deflected goalwards by striker David Connolly, only for Peter Brezovan to make a fine save.
If manager Nigel Adkins was frustrated by that chance not being converted, he will have been even more dismayed midway through the opening period.
Connolly and Lallana were instrumental once more, linking up before the latter found the unmarked Guly Do Prado, who somehow managed to hit over from close range.
That did not stop Lallana, though, with the midfielder continuing to pose all sorts of problems as he was denied a goal when his effort appeared to cross the line, prior to Steve Cook's clearance.
Seemingly spurred on by the apparent injustice, Saints picked up where they left off at the start of the second half as a loud penalty appeal was turned down after Lambert went down under a challenge.
But their cause became somewhat more difficult soon after when Lambert - who has picked up just three bookings in the last two years - was dismissed after an altercation with Adam El-Abd.
The hosts seemed instantly spurred on by their one-man advantage and Saints were left thanking goalkeeper Davis after he impressively denied LuaLua.
However, he was left picking the ball out of the back of his net moments later as Forster-Caskey - on his full debut - slotted home after Davis had initially kept out LuaLua's stinging effort.
Sparrow's wonder goal then added to the hosts' joy and he added another by firing into the top corner from just inside the area.
The sides finished with 10 men apiece after Gordon Greer was sent off with three minutes to go for an off-the-ball incident, but it mattered little.