Moussa Djenepo struck for the first time since last September to give the Saints the lead just before half time to give the hosts a deserved lead, having dominated the first period.
Baggies keeper Sam Johnstone produced some fine saves to keep his team in the game, but he could only stand and watch Romeu’s superb strike sail into the top corner midway through the second half to seal the win.
After the drubbing by Tottenham, the Saints have responded with consecutive wins and successive clean sheets, responding in the perfect manner.
Having named an unchanged starting line up from that which won at Turf Moor, the Saints started brightly as Stuart Armstrong picked out the run of Ryan Bertrand but his effort was beaten away by Johnstone.
Ralph Hasenhuttl’s side were in control and were creating chances, and could have taken the lead 15 minutes in. Kyle Walker-Peters burst down the right and would have forced an own goal if not for a fine reflex save from Johnstone, who adjusted in the nick of time after the low cross was deflected towards his own goal by Semi Ajayi.
The move stayed alive after the save, and Che Adams was first to react to the loose ball but Johnstone recovered to produce a great save from point-blank range to turn his effort over the bar.
The Albion stopper continued to impress, saving brilliantly to deny Danny Ings from breaking the deadlock when he met James Ward-Prowse’s free-kick before he was finally beaten five minutes before the interval.
Adams found Ings on the right, who tried to return the favour but his pass deflected kindly to Djenepo, who turned onto his left foot and fired a low drive into the bottom corner from just inside the penalty area.
For their first half dominance, the Saints were only a goal up and West Brom began to pose a greater threat after the break.
Alex McCarthy was called into action when Grady Diangana’s low shot was deflected off Walker-Peters, but the Saints keeper’s outstretched foot turned the ball away.
But the Saints gave themselves breathing space with a sensational second goal after 69 minutes. Armstrong whipped in a great ball from the left and Romeu found a gap in the area, and the Saints midfielder thumped a volley that flew past Johnstone and into the top corner.
The strike seemed to dampen West Brom’s spirits, with the Saints almost adding a third late on. First Walker-Peters side-footed an effort off target before Ward-Prowse forced Johnstone into another good save.