Martin Olsson's own goal and second-half efforts from Marc-Antoine Fortune and Liam Ridgewell earned the Baggies three points.
Olsson sliced his clearance past Rovers goalkeeper Paul Robinson for the opener after seven minutes before Fortune and Ridgewell wrapped up the points for Roy Hodgson's side.
Rovers substitute Anthony Modeste was harshly sent off for violent conduct in injury time after pushing Albion defender Billy Jones.
It was West Brom's first win in five league games and took them to the 39-point mark, while for Rovers a third successive defeat means they remain in the bottom three.
The visitors enjoyed large spells of possession with Junior Hoilett impressing and causing problems.
But Blackburn found on-loan Albion goalkeeper Ben Foster in inspired form and he produced several fine saves.
Fortune again led the Albion attack in fine style with his power and pace and deserved his fifth goal of the campaign, while Youssouf Mulumbu anchored the midfield.
Albion were the first to threaten and Jonas Olsson's header flew past the post from a Chris Brunt corner.
The home side applied the majority of the early pressure and Gareth McAuley had a shot blocked on the edge of the box.
West Brom forced four corners in the first seven minutes - and from the last of them they took the lead. McAuley headed Brunt's ball into the box back across goal and Rovers defender Martin Olsson only succeeded in slicing the ball past Robinson into his own net.
Rovers started to get a foothold in the game and leading scorer Ayegbeni Yakubu almost played in David Dunn with a reverse pass but Graham Dorrans was alert to the danger and tidied up.
Martin Olsson tried to make amends for his error with an inviting cross for Bradley Orr to run onto, but he could not keep his far-post header down.
Scott Dann powered a header straight at former Birmingham team-mate Foster from Orr's cross from the right flank, before Hoilett curled an effort wide from 20 yards out and Foster clung onto Dunn's low attempt.
The hard-working Fortune teed up Mulumbu, but his shot lacked power and Robinson saved comfortably.
Blackburn began the second half on the offensive and Morten Gamst Pedersen made clean contact on a Jason Lowe centre but his header flew straight at Foster.
Dann became the first player to be booked after 51 minutes for holding back Peter Odemwingie.
Mulumbu's misdirected pass almost presented Yakubu with an equaliser but Foster reacted quickly and raced out of his area to hack the ball clear.
The former England goalkeeper then produced a superb double save to keep his side in front, first getting down to his right to deny Yakubu and then reacting quickly to block the follow-up effort from Orr.
Rovers were now in the ascendancy and Yakubu was only just too high with a powerful drive while Foster held onto a long-range attempt by the impressive Hoilett.
But against the run of play Fortune doubled Albion's lead after 68 minutes.
Brunt dispossessed Yakubu and picked out Fortune with a low cross. He had time to steady himself before driving the ball past Robinson.
Rovers were almost caught on the counter-attack but Mulumbu failed to pick out the unmarked Fortune when Albion had a two-to-one numerical advantage.
Hoilett continued to probe for Rovers but Foster held onto his curling attempt, and with five minutes left Albion added a third as Ridgewell scored his first for the club when he headed home an inswinging Dorrans free-kick. Modeste's act of frustration in the final seconds capped a miserable day for Steve Kean's side.