The meeting between the two play-off hopefuls ends in a draw.
The Baggies looked to be heading for a seventh straight home win through Jayson Molumby's header.
But Ben Brereton Diaz's late free-kick means West Brom miss the chance to move back into the top six.
Blackburn have drawn their past four and are now five without a win in the league. West Brom have one win in four in the Championship.
Middlesbrough have been absolutely outstanding. When that early goal went in your thought it was going to be tough because Sheffield United were on the front foot.