Story of the match
The hosts started the brighter of the two, and they could have quite easily been given a penalty in just the third minute, when Ben Brereton went down appearing to be pushed by the Chelsea loanee.
Continuing their early dominance, Brereton and Tyrhys Dolan particularly stood out in the first 20 minutes, with their pace and power causing the Swansea backline a number of problems.
After securing the ball from a rare spell of Swansea possession, Rovers nearly broke forward to perfection, but Brereton's heavy touch allowed the visitors to recover.
A minute later, Bradley Dack opened the scoring for the hosts, latching onto Tom Trybull's brilliant through ball and slotting home through Freddie Woodman's legs.
In the 40th minute, Andre Ayew netted an equaliser from the penalty spot, after Sam Gallagher was adjudged to have fouled Jay Fulton - his third converted spot-kick in as many games.
Brereton started the second half as lively as he was in the first, and he nearly restored Rovers' lead in the 47th minute but his lobbed effort bounced the wrong side of the post.
In the 55th minute, Dack had half an opportunity to double his tally but his strike from John Buckley's cut-back was deflected out for a corner.
Harvey Elliott was introduced in the 70th minute and added an extra dimension in Rovers' pursuit of earning all three points.
The Liverpool loanee made an instant impact, linking with his frontmen and was unlucky not to find a Blackburn shirt with his drilled cross, after excellent play to get in behind.
In the 80th minute, Ayew nearly took advantage of a rare Swansea break, curling an effort over the bar after good work on the right flank.
Both sides struggled to create anything meaningful in the concluding stages of the match and the sound of the final whistle meant that Swansea would stay in third place.
The hosts will certainly feel hard done by with just a point. They enjoyed a lot more possession in Swansea's final third and created enough chances to take all three points. It is another point towards their promotion push, but they will need to improve if they are to secure promotion back to the Premier League.
Being 12 points from the play-offs and 12 off the relegation zone, it seems that Blackburn are set for another uneventful Championship conclusion.
For the hosts, 19-year-old Thryhs Dolan had an excellent game in an unfamiliar central striker role. His trickery and explosivity made him a difficult man to mark all night. He linked well with Gallagher and Brereton and proved to be a brilliant option in Adam Armstrong's absence.
In an uninspiring performance from the Swans, Andre Ayew remained his classy self in the rare occasions that he received possession. Ultimately, he was the one who scored the all-important equaliser