Bradley Johnson handed Blackburn a lifeline just before half-time however and Rovers were on top for most of the second half, but they could not find an equaliser, despite having an effort disallowed and hitting the post.
But virtually the rest of the first half belonged to West Brom.
The home side went desperately close when right back Darnell Furlong crossed and Pereira's diving header was inches wide.
But West Brom's pressure was rewarded in the 31st minute when they went ahead.
A chip from Phillips hit the bar from Furlong's pull back, and Pereira laid it back to Livermore, who sidefooted in.
After Charlie Austin sliced wide from another Pereira cross, the scoreline was given a more emphatic look five minutes before the break.
Diangana left Darragh Lenihan for dead on the left and raced towards goal before dinking the ball over Walton from a tight angle for his third of the season.
Out of the blue, Rovers scored in the first minute of time added on at the end of the first half.
The switch appeared to pay off in the 57th minute when Blackburn had the ball in the net.
Downing's free kick was deflected against the bar by Semi Ajayi, Lenihan challenged Johnstone in the air and the ball dropped into the net. But referee Tony Harrington ruled Lenihan had fouled the keeper.
Rovers were a fraction away from equalising in the 67th minute when Downing hit the post with a first-time effort from Dack's free kick.
But Albion responded with a curling effort from Pereira that flew inches over from Diangana's cross.
Phillips twice threatened for the Baggies late on, his header smothered on the line by Walton before he blazed over from point-blank range.