In a pulsating opening 60 seconds, the Baggies hit the woodwork and registered three shots including Alex Mowatt's spectacular volley - his second goal this week.
Matt Phillips doubled the lead from close range in first-half stoppage time as Albion suffocated their hosts in the Sky Bet Championship contest at Ewood Park.
Rovers were given hope after Ben Brereton Diaz profited from a Sam Johnstone error but the scoreline was not a true reflection of the dominance of Valerien Ismael's men. The Baggies hit the woodwork four times and saw Thomas Kaminski produce superb saves to twice deny Callum Robinson and Karlan Grant.
West Brom's record of scoring at least two goals in each game this season proved crucial and they are one of only three teams on 10 points.
Blackburn's own unbeaten run was ended but they displayed enough character against a superior team to provide encouragement.
Leighton Clarkson made his debut after joining his hometown club on loan from Liverpool.
Phillips, Albion's only change from the 4-0 rout of Sheffield United, made a blistering start, dispossessing Darragh Lenihan in the first minute and crossing for Jake Livermore - whose low drive was brilliantly saved by Thomas Kaminski before his follow-up cannoned back off the woodwork.
But Phillips picked up the loose ball and his next cross was met by Mowatt, who sumptuously volleyed into the top left corner from 18 yards.
Kaminski brilliantly tipped over Robinson's dipping 25-yard effort as the visitors dominated, before Clarkson's inventive pass gave Blackburn their first sight minutes before half-time, but Brereton Diaz wastefully fired over.
Missing that rare chance proved costly as the visitors' lead was doubled in first-half added time.
Moments after his header clipped the bar, Phillips earned redemption after Grant was released on the left and his inch-perfect cross provided Phillips with a simple tap-in for his first goal this season.
Grant majestically weaved into the box just after the restart but was thwarted by Kaminski's sharp low save.
It was vital for Rovers, who were gifted a foothold back into proceedings in the 51st minute when Johnstone's attempted clearance hit Brereton Diaz, leaving the Chilean with an open goal to slot in his third this term.
Substitute Grady Diangana released Grant midway through the half but Kaminski spread himself to block the ball, which squirmed off the post to safety.
Robinson's rasping 20-yard resulted in the best of Kaminski's saves as he parried strongly away low to his right.
The goalkeeper could do nothing 10 minutes from time to stop Darnell Furlong's thumping header - but the post kept Rovers in the contest.
Albion, though, held on for a battling win.