The Championship’s leading scorer netted either side of half-time at Selhurst Park to sink Palace and send Saints three points clear at the top.
Lambert has now hit 87 goals in three years for the south-coast side and the prolific 30-year-old, who has spent his entire career in the lower divisions, looks certain to finally get a crack at the top flight.
With five games to go Nigel Adkins’ side are on the brink of back-to-back promotions, sitting three points ahead of Reading – who play Brighton on Tuesday – while crucially also keeping third-placed West Ham at arm’s length.
By contrast Palace’s season, which has included a run to the Carling Cup semi-finals, is fizzling out after a third straight defeat.
The injury-hit Eagles almost grabbed a shock early lead when Kagisho Dikgacoi’s header was tipped over the crossbar by Kelvin Davis.
Saints goalkeeper Davis came to his side’s rescue again 10 minutes before half-time with a stunning save to deny Kyle de Silva.
The locally-born 18-year-old, thrown in for his full league debut for patched-up Palace, almost capped it with a superb run and shot from 20 yards but Davis stuck out a hand to palm it over.
Yet somehow, Palace went in behind at the break – thanks to the irrepressible Lambert.
The striker had been feeding off scraps for the first half an hour, until he suddenly burst into life with a low shot from 18 yards which was deflected narrowly wide.
From the corner Lambert rifled the ball in the net but the whistle had already gone for a push by former Eagle Jose Fonte.
But in the 39th minute another Palace old boy, Danny Butterfield, crossed from the right, defender Paddy McCarthy missed it but Lambert did not, climbing above Nathaniel Clyne to bury his header past Julian Speroni.
There was time for Palace striker Chris Martin to blaze over before the interval.
But Lambert ended any hopes of a Palace revival 10 minutes after the restart with another well taken strike.
Played in by Jack Cork, Lambert skilfully sidestepped McCarthy on the edge of the area before arrowing a low drive into the far corner.
To Palace’s credit they kept going forward and Davis saved well again from Sean Scannell’s deflected shot.
But nothing was going to deny Saints, who are marching on towards a return to the Premier League seven years after they left.