Blackburn top scorer Ben Brereton Diaz went off with a foot injury as new West Brom boss Steve Bruce picked up a point from his first home game in charge.
The hosts had the best chance of a low-key first half, Karlan Grant failing to connect with Darnell Furlong's cross.
Both sides had offside goals ruled out before 20-goal Brereton Diaz came off on 70 minutes after an attempted shot.
The Baggies almost won it late on but sub Tyrhys Dolan acrobatically cleared Adam Reach's header off the line.
After starting with defeat by Sheffield United five nights earlier, Bruce's first point as Albion boss was just desserts for a committed home performance.