West Brom missed a wonderful chance to climb clear of the relegation zone after letting slip a lead at home.
Kieran Richardson gave the hosts the advantage with a stunning free-kick around the Blackburn wall and beyond a flailing Brad Friedel on 32 minutes.
But Rovers responded to two good Neil Clement efforts and took control.
Jon Stead had earlier hit a post and after Brett Emerton swept in a Morten Gamst Pedersen cross, Pedersen and Robbie Savage went close as well.
The point was enough to see West Brom climb a place to 18th, but all three would have seen them move two points clear of the relegation zone.
However, while they had been worth their lead, they will be grateful for a point as they let the initiative slip.
After Emerton's equaliser, Paul Robinson made a last-ditch tackle to deny Pedersen and Russell Hoult saved a Savage volley from point-blank range.
That there was so much goalmouth action came as a surprise considering the hosts boasted the worst home scoring record in the Premiership and the visitors came into the game with the worst return on the road.
For a time it looked as if even one goal would prove elusive, particularly when the referee waved away penalty appeals after Andy Todd grappled Kevin Campbell to the ground.
But then Richardson stepped up after Ryan Nelson fouled Geoff Horsfield on the edge of the area, and the 20-year-old made the most of the promising position.
After a two-step approach, he bent a blistering shot into the top corner of the net.
It was the first goal Blackburn had conceded in 439 minutes of Premiership football.
Rovers responded, but instead of hitting the net Stead saw an effort cannon off the post after pouncing on Marcus Albrechtsen's half-clearance with a sharp half-volley.
Clement missed a wonderful chance to make it two when he failed to make proper contact with Richard Chaplow's corner at the back post, and then saw a fierce, driven free-kick well saved by Friedel.
Hoult was also called on to make a telling contribution when he maintained West Brom's lead with a brave save at Pedersen's feet after a wonderfully-flighted pass from Tugay.
It was to prove the pre-cursor to a change in the tone of the match as Rovers exerted greater authority on proceedings.
West Brom's chances all but dried up and Clement's failure to bury a floated Ronnie Wallwork free-kick at the back post on 85 minutes could haunt their survival effort, particularly with matches to come against Arsenal and Manchester United.
West Brom: Hoult, Albrechtsen, Gaardsoe, Clement, Robinson, Gera, Wallwork, Richardson, Chaplow (Kanu 63), Campbell (Scimeca 63), Horsfield (Earnshaw 79).
Subs Not Used: Moore, Kuszczak.
Booked: Horsfield, Robinson, Scimeca.
Goals: Richardson 32.
Blackburn: Friedel, Neill, Todd, Nelsen, Matteo, Emerton, Reid, Mokoena (Tugay 56), Savage (Gallagher 87), Pedersen (Thompson 83), Stead.
Subs Not Used: Flitcroft, Enckelman.
Booked: Matteo, Pedersen, Todd.
Goals: Emerton 64.
Att: 25,154
Ref: S Bennett (Kent).