The veteran striker, 37, ran on to a long clearance and steered a shot past keeper Jason Steele in the 88th minute.
Rovers' Ben Marshall had the only effort on target in the first half, a free-kick that went straight at home keeper Frank Fielding.
Chances continued to be at a premium after the break until Wilbraham secured City's fifth home win of the season.
The home fans stood in tribute to the late Gerry Gow in the 64th minute, and were on their feet again when their penalty appeals were turned down after Scott Golbourne's shot appeared to hit Darragh Lenihan's arm.
Marvin Emnes saw a shot blocked as Rovers slid to a fifth away league defeat of the season.
City, who have now won four of their last six games, move above Birmingham into the play-off spots in sixth, while Blackburn drop back into the bottom three.
Bristol City boss Lee Johnson:
"It was a tough game for us. I consider Blackburn to be in a false position and they will be very disappointed not to have taken something.
"I was happy to reach half-time not one or two goals behind. But we were more like ourselves in the second half and deserved the bit of luck with the goal.
"Blackburn had blocked a lot of our shots and by the law of averages a deflection was due to go our way."
Blackburn Rovers manager Owen Coyle:
"I am gutted for the players and our travelling supporters. A performance like that would normally earn you three points, let alone one.
"We should have been ahead at half-time and my only concern is the small errors that can make all the difference in a close game.
"The goal came from our corner and one long ball forward after we concede a free-kick. We should have defended the situation better, but it was still an unfortunate deflection.
"I can't recall Jason Steele having to make a difficult save. The level of performance was so high and it's a huge disappointment to come away with nothing."
Match ends, Bristol City 1, Blackburn Rovers 0.
Second Half ends, Bristol City 1, Blackburn Rovers 0.
Charlie Mulgrew (Blackburn Rovers) wins a free kick in the defensive half.
Foul by Aaron Wilbraham (Bristol City).
Joe Bryan (Bristol City) wins a free kick on the right wing.
Foul by Craig Conway (Blackburn Rovers).
Attempt saved. Ben Marshall (Blackburn Rovers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Corry Evans.
Charlie Mulgrew (Blackburn Rovers) is shown the yellow card.
Goal!  Bristol City 1, Blackburn Rovers 0. Aaron Wilbraham (Bristol City) left footed shot from the centre of the box to the bottom right corner. Assisted by Lee Tomlin following a set piece situation.
Lee Tomlin (Bristol City) wins a free kick in the defensive half.
Foul by Corry Evans (Blackburn Rovers).
Corner,  Blackburn Rovers. Conceded by Scott Golbourne.
Attempt missed. Tammy Abraham (Bristol City) header from the centre of the box is close, but misses to the left following a corner.
Corner,  Bristol City. Conceded by Darragh Lenihan.
Attempt blocked. Tammy Abraham (Bristol City) right footed shot from the centre of the box is blocked. Assisted by Gary O'Neil.
Corner,  Blackburn Rovers. Conceded by Scott Golbourne.
Attempt missed. Ben Marshall (Blackburn Rovers) left footed shot from outside the box is just a bit too high. Assisted by Jason Lowe.
Offside, Blackburn Rovers. Corry Evans tries a through ball, but Hope Akpan is caught offside.
Foul by Joe Bryan (Bristol City).
Craig Conway (Blackburn Rovers) wins a free kick on the left wing.
Korey Smith (Bristol City) wins a free kick in the defensive half.
Foul by Marvin Emnes (Blackburn Rovers).
Attempt blocked. Joe Bryan (Bristol City) left footed shot from the right side of the box is blocked. Assisted by Tammy Abraham.
Attempt missed. Charlie Mulgrew (Blackburn Rovers) left footed shot from outside the box misses to the right.
Foul by Aaron Wilbraham (Bristol City).
Darragh Lenihan (Blackburn Rovers) wins a free kick in the defensive half.
Substitution, Blackburn Rovers. Hope Akpan replaces Danny Guthrie.
Substitution, Bristol City. Joe Bryan replaces Luke Freeman.
Foul by Danny Guthrie (Blackburn Rovers).
Korey Smith (Bristol City) wins a free kick in the defensive half.
Attempt missed. Korey Smith (Bristol City) right footed shot from the right side of the box is close, but misses to the right.
Delay over. They are ready to continue.
Delay in match Luke Freeman (Bristol City) because of an injury.
Attempt saved. Tommie Hoban (Blackburn Rovers) header from the centre of the box is saved in the bottom left corner. Assisted by Craig Conway with a cross.
Attempt blocked. Marvin Emnes (Blackburn Rovers) right footed shot from a difficult angle on the right is blocked. Assisted by Ben Marshall.
Corner,  Blackburn Rovers. Conceded by Aden Flint.
Corner,  Bristol City. Conceded by Sam Gallagher.
Substitution, Bristol City. Taylor Moore replaces Adam Matthews.
Substitution, Bristol City. Aaron Wilbraham replaces Jamie Paterson.
Corner,  Bristol City. Conceded by Darragh Lenihan.
Aaron Wilbraham struck late on as Bristol City edged past Blackburn Rovers at Ashton Gate.