The hosts controlled the game for large periods at the University of Bolton Stadium, but were unable to find the cutting edge to unlock Rovers’ stern defence.
Tony Mowbray’s men had to work for the three points, though. David Raya was forced into an unbelievable save to tip to Josh Magennis’ header over the bar.
The Northern Ireland international also saw an effort cleared off the line by Blackburn skipper Charlie Mulgrew.
But Dack’s scrappy opener inside half an hour was enough to move the visitors up to ninth, level on points with Brentford in the play-offs.
However the situation is less than rosy for Bolton, one win in eight games leaves them sitting 16th, and they may begin to start looking over their shoulders after an awful run of form.
Trotters boss Phil Parkinson felt his side deserved more: “It’s a game we should’ve got something out of. Some of the football we played was excellent.
“The honesty, endeavour and bravery to keep on playing was fantastic but we just lacked that bit of quality in the final third to get something out of the game.
“We’ve got in so many good positions but not been able to produce when it matters. We need to be more clincal.”
Wanderers go into the international break in desperate need of time to regroup and get their injured players back to full fitness.
Parkinson hopes to welcome back Sammy Ameobi, Ben Alnwick and Andrew Taylor after the international break, with Ameobi and Taylor making particularly good progress in their recoveries.
New signing Lloyd Dyer made his debut when he replaced Craig Noone with 20 minutes to go, but was unable to make a significant impact.