Saints stretched their winning run at home to 20 consecutive matches.
Lambert opened the scoring with a fine header just after half-time and took his tally for the season to 14 with a brace of penalties.
Defeat capped a tough week for Brighton manager Gus Poyet after he waded into football’s racism row.
In the first half, Brighton defended with the same conviction with which Poyet had defended his fellow Uruguayan Luis Suarez.
But they fell apart after the interval and had Mauricio Taricco sent off for dissent in the aftermath of the first penalty decision.
These two south-coast sides have never been traditional foes, but there is now a distinct edge to proceedings after they were slugging it out at the top of League One last season.
Brighton won that particular race but Saints are out in front this time, having not failed to win on their own patch since losing to Manchester United in the FA Cup in January.
They almost took a third-minute lead when Guly Do Prado turned and shot inside the area but his effort struck Gordon Greer, and referee Peter Walton waved away appeals for handball.
Guly and Richard Chaplow then just failed to get on the end of clever flicks from Lambert, who also had a header kept out by Seagulls keeper Steve Harper.
Brighton threatened only sporadically in the first half with Lewis Dunk heading an early chance over the crossbar and Ryan Harley also firing too high.
But Saints finally found a way through the resolute Brighton rearguard four minutes after the interval.
Right-back Frazer Richardson cut inside and swung in a deep, left-footed cross to the far post where Lambert was lurking.
The big striker still had plenty to do but he rose above two Seagulls defenders and powered his header past Harper.
Walton was unmoved by another penalty appeal when Harper tripped Dean Hammond, but the referee did point to the spot in the 57th minute when Dunk brought down Jose Fonte.
Dunk was booked for the foul but Taricco’s protests brought the 38-year-old Argentinian, Poyet’s assistant manager, a straight red card.
Lambert was denied his hat-trick by the fingertips of Harper, but only briefly.
His moment came in the 69th minute, again from the spot after he was felled by Inigo Calderon.
He had two cracks at it after Walton ruled out his first effort, but stroked his second effort home to keep Saints five points clear at the top.