It was the home side who started the better and they took the lead after just seven minutes when Blackburn defender Martin Olsson could only only head into his own goal after Gareth McAuley had risen highest from a corner.
West Brom continued to look the stronger, however, with Peter Odemwingie causing all sorts of problems to the away side's defence.
Odemwingie might have doubled the home side's lead just before the 30-minute mark, but he fired high and wide.
Blackburn improved as the half progressed into its latter stages, with Morten Gamst Pedersen causing problems with his direct running.
Junior Hoilett passed up the away side's best chance of the half moments before the break when he fired wide from outside the box.
Blackburn might have levelled the match moments into the second period, but Pedersen's header never had enough power to worry Foster who collected with ease.
Foster kept the home side ahead with a fine save from Dann, before Yakubu fired over the bar after 57 minutes.
Blackburn continued to dominate the second period, and Jason Lowe fired over just before the 60-minute mark in the match, with Hoilett impressing for Rovers.
Hoilett remained Blackburn's biggest threat, but the second goal deflated Steve Kean's side, and they conceded a third late on when Liam Ridgewell headed home.
Blackburn remain in the relegation zone with six games remaining.