Rovers had more than their fair share of chances in the first half but Wes Thomas had headed Blackpool in front by the time Simon Vukcevic rattled the post for the visitors.
Henning Berg's side were unable to muster anything like a similar threat in a second half of few chances, and switched off late on to let former Rangers defender Kirk Broadfoot net a first Seasiders goal.
Appleton has now masterminded two wins from the last three outings, having begun his tenure as Ian Holloway's replacement with four consecutive draws.
The visitors were quickest out of the blocks and Seasiders defender Craig Cathcart required a last-ditch challenge to deny Jordan Rhodes from Colin Kazim-Richards' cross, before Matt Gilks made saves in quick succession to thwart Rhodes and Vukcevic.
It was therefore against the run of play when Nathan Delfouneso crossed from the left for Thomas to glance in with the assistance of a statuesque Blackburn defence in the 24th minute.
Dickson Etuhu had a chance to bring Blackburn level after the half hour but shot wide from Josh King's clipped cross as Blackpool failed to fully clear a corner.
But it was almost all-square at the break as Vukcevic rattled the post with a shot on the turn.
In the second half England U21 winger Ince appeared the most likely source of extending Blackpool's lead and, after breaking free of the Rovers defence to test Jake Kean low to his right, he exchanged passes with Bob Harris for the latter to fire over in the 65th minute.
Harris managed to extend Kean when the Rovers keeper pushed a rasping free-kick behind, but the points were made safe from the resulting corner.
Tiago Gomes' outswinging delivery from the right found Broadfoot to thump home unmarked with nine minutes to play.
Gael Givet thought he had a consolation but was flagged offside before Scott Dann almost compounded Rovers' misery by heading against his own post in stoppage time.