Despite their recent impressive results, on Tuesday they fell behind in the 37-minute thanks to Bradley Dack’s low strike from Tom Trybull’s assist.
Cooper’s men were given a chance to equalise four minutes later when Jay Fulton was fouled by Sam Gallagher in the goal area.
Their Ghanaian star stepped up to score his 14th goal of the 2020-21 campaign, as goalkeeper Thomas Kaminski could not stop the strike down the middle.
In the second half, Blackburn came out stronger, but they were unable to find the net despite their incessant attacks.
The game ended on a no winner no vanquished note as Swansea now boast of 66 points from 34 matches, level with second-placed Watford with a game in hand.