The visitors took a thoroughly deserved lead through Marc-Antoine Fortune, who bundled the ball over Artur Boruc, after Lukaku had flicked a corner back into the six-yard box.
An excellently taken strike from the giant Belgian doubled the Baggies' lead, before Saints' substitute Gaston Ramirez and the visitors' Fortune were both sent off by referee Robert Madley, making his Premier League debut.
Shane Long netted his first goal in nine games shortly afterwards to seal the points for the visitors, but there was still time for Danny Fox to be dismissed in what turned out to be an unforgettable Premier League introduction for rookie referee Madley.
The Baggies were much the better side right from the word go with Lukaku, who came close in the opening five minutes, having two more efforts well saved by Boruc.
The on-loan Chelsea star had a big hand in the opening goal, keeping a corner alive by winning a header which Fortune did well to stab goalwards under pressure, and the ball just crawled over the line in time before it was cleared.
With his side in the ascendancy, Lukaku's chance at the end of the opening period was the best of the lot when, after an intricate team move, the young Belgian found Boruc a formidable opponent again as he saved well low to his right.
Nathaniel Clyne, who had the hosts' only effort on goal in the first half, almost netted a surprise equaliser early in the second period, digging a shot out of nowhere which evaded Ben Foster in the Baggies' goal, but came back off the crossbar.
The meagre resistance that the Saints were offering was soon halted by the killer second goal from the Baggies. Fortune held the ball up well, turned and played a perfect through pass for Lukaku to latch onto, and the 19-year-old made no mistake this time, rounding Boruc and slotting the ball into the empty net.
The home side seemed to lose all composure, which was evident as Ramirez received a red card for a needless swing of the arm at Liam Ridgewell, and Fortune joined him after unnecessarily raising his hands in the fracas that ensued.
The result was put beyond doubt when Long raced through and placed his finish underneath a helpless Boruc after more good work from Lukaku to provide the assist.
Despite desperately needing a response, the Saints' ill-discipline continued, as Fox saw red for a dangerous two-footed lunge of Steven Reid.
After going six games unbeaten, the scoreline did come somewhat out of the blue, but the impressive Baggies have now accumulated their highest points total in the Premier League, and the Saints will not suffer too much, as they are practically safe with three games to go.