Dunn opened the scoring in the first half with a powerful left-footed finish from the edge of the area, and Hanley - the captain after Scott Dann's departure to Crystal Palace - headed in a second late on.
The result keeps Rovers five points behind sixth-placed Reading and ended a run of four games without a win in all competitions.
It extended Blackpool's horrendous run of form, and they have now taken just two points from the last available 36 in the league.
Blackpool interim player-manager Barry Ferguson made three changes following the defeat at Reading, which included a debut for Faris Haroun. Fellow deadline-day signings Andy Keogh and Stephen Dobbie started on the bench.
Blackburn boss Gary Bowyer made two alterations after the draw at Barnsley, with Chris Taylor and Todd Kane drafted in. New purchases Bryan Dabo and Craig Conway were among the substitutes.
Blackpool had lost their previous six away league games and Isaiah Osbourne missed a good chance to change the tide after 11 minutes when he powered his header over having been left unmarked.
But it was Blackburn who went in front after 19 minutes through Dunn, who picked the ball up 30 yards out and was able to advance forward with minimal resistance before lashing in a low drive from 18 yards for his third goal of the season.
Chris Basham almost drew the visitors level with a speculative 30-yard drive that swerved in the horrendous East Lancashire conditions and forced Paul Robinson into an improvised low save.
The poor conditions meant both sides struggled to create chances of note, though Steve Davies should have done better when he swivelled to find space after 55 minutes but then found the side-netting with his shot.
Jordan Rhodes has not scored since New Year's Day and almost ended that drought a minute later but he glanced Tommy Spurr's left-wing cross wide.
His strike partner, Rudy Gestede, had scored in four of his previous five league games and did well to direct a header towards goal after 77 minutes but failed to hit the target.
At the other end, the introductions of Keogh and Dobbie gave Ferguson's men fresh impetus and the latter weaved away from Blackburn's attention before letting fly with a crisp, left-footed effort that deflected over with Robinson struggling.
But Rovers effectively finished the contest with nine minutes remaining when Hanley headed Conway's corner into the ground and over Matt Gilks.
Conway's brief cameo almost saw him set up another goal in the final minute but Rhodes could only head over after the former Cardiff man chipped a cross to him.