The visitors took the lead after just eight minutes as the Saints failed to clear their lines from a corner. Marc-Antoine Fortune's initial shot was saved by Artur Boruc, but the ball bounced back off the West Brom striker and trickled over the line.
Nathaniel Clyne had a good chance to pull his side level just after the half-hour mark when he found space to shoot from inside the box, but his effort was well saved by Ben Foster.
Clyne came close again 10 minutes after the break when his shot from a tight angle took a deflection, sending it onto Foster's crossbar.
West Brom doubled their lead in the 66th minute when Fortune's through-ball found Lukaku, who showed good composure to take it round Boruc and slide it into the empty net.
Both sides were reduced to 10 men with 20 minutes left on the clock when Gaston Ramirez elbowed Shane Long, who was holding him back as he looked to break free. In the aftermath, Fortune raised his hands to Ramirez, resulting in red cards for both players.
The Baggies sealed all three points in the 77th minute when Long raced away from Jos Hooiveld before beating Boruc at his near post.