Smallwood’s 84th-minute curler from outside the box was enough to clinch all three points and keep the heat on second-placed Shrewsbury as Tony Mowbray’s men made it 16 games without defeat.
Rovers outclassed Fleetwood in the first half with a moment of magic in the 27th minute from Bradley Dack giving them a deserved lead as he rolled the ball under Chris Neal from an angle on the left.
Dominic Samuel rattled the side netting and Derrick Williams’ header crashed into the bar but the visitors only took a 1-0 lead in at the break.
Fleetwood came out all guns blazing in the second half and after Danny Graham had hit the woodwork for Blackburn, Conor McAleny pounced.
The forward seized on a poor Charlie Mulgrew back pass and coolly danced past David Raya before rolling the ball into an empty net in the 55th minute.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.