Steven Fletcher scored his 10th league goal of the season early on and the man he was replaced by, Atdhe Nuhiu, headed home with his first touch in the 60th minute.
Blackburn substitute Craig Conway struck back in the 72nd minute but right-back Dominic Iorfa settled Owls nerves seven minutes later as he made it 3-1 in front of the 24,608 crowd. Substitute Marco Matias made it 4-1 but Blackburn showed resolve as Elliott Bennett scored to make it 4-2 in the 88th minute.
The victory meant Wednesday had made it 20 points out of 30 under their new head coach and avenged a defeat by the same scoreline at Ewood Park.
Owls chief Bruce made just one change from the side that started in midweek against Bolton Wanderers. Sam Winnall got the nod for his first Wednesday start since August, 2017, partnering Fletcher up front with Nuhiu dropping to the bench.
Blackburn gave starts to Joe Rothwell and Corry Evans with Amari'i Bell failing to overcome an injury suffered in the midweek win against Wigan and Adam Armstrong given a substitute's role.
The Owls suffered an early blow when Sam Hutchinson limped off with a hamstring problem and was replaced by Joey Pelupessy.
However, they soon got the tonic they required when Adam Reach sent Iorfa down the right to produce a low cross which Fletcher, who had nipped ahead of Tyler Maglorie, tapped in from inside the six-yard area to make it 1-0 in the 10th minute.
The Owls continued to exploit space out wide and after a free-kick had been partially cleared, Michael Hector headed against a post from Reach's cross.
Blackburn had a chance on 30 minutes when Rodwell robbed Iorfa, made ground and tried to thread the ball through to Dack but Westwood was first to react, smothering the ball.
Fletcher was first in the book for what seemed an inadvertent trip on Harrison Reed, whose free-kick was cleared.
Westwood kept it 1-0 when going down to his left to palm away Dack's shot from 14 yards and that is how it stayed until the break.
No changes were made at the break and Winnall went in the book for a late challenge on Derrick Williams.
Graham headed wide from six yards from Rothwell's cross after switching play from the left before Matias replaced Winnall and Blackburn's Conway came on for Reed in the 55th minute. Fletcher gave way to Nuhiu three minutes later.
The move paid swift dividends, Reach winning a free-kick 34 yards out in the 60th minute and Bannan clipping the free-kick for Nuhiu to head home from six yards.
Blackburn made a double switch, Armstrong and John Buckley replacing Graham and Evans, in a bid to retrieve at least a point.
Tony Mowbray's side hit back as Rothwell burst down the middle and played the ball into space for Conway, coming in from the right, to make it 2-1 in the 72nd minute.
Their hopes evaporated as Aarons won a fee-kick outside the left corner of the area and Bannan again chipped the free-kick into the danger area and it fell for Iorfa to fire home from seven yards.
Hector made an important block from Dack before Nuihu broke down the right and the ball was moved across for Bannan to set a low drive for Matias which squirmed under the body of David Raya to make it 4-1.
Rovers were not finished and Bennett cut inside Hector to drill the ball home inside Westwood's right-hand post before time ran out.
"To score four was great and we've got to be happy, although we went a bit sloppy towards the end and we nearly got punished," Bruce said afterwards.
"We went deep too quickly and I wish we hadn't conceded the way we did. We should have made it more comfortable than we did, but overall I'm delighted.
"It's fair to say we got our goals at the right time. Blackburn are a threat and they caused us problems.
"It was a horrendous afternoon - the conditions made it very difficult for the players."
Blackburn manager Tony Mowbray said: "There were lots of positives for us. I thought we gave them lots and lots of problems.
"The very obvious problem for us is that we have a team of kids at the back at the moment. We've got three international central defenders missing and the left-back is not available.
"Steven Fletcher and Nuhiu have physicality in the box from dead balls which hurt us. Apart from that, I thought we performed pretty well today and gave them lots of problems.
"We could have scored lots of goals today but what we couldn't do was deal with their free-kicks into the box because we've got no physicality, which makes it very difficult.
"We have to accept that and we'll be stronger in a couple of weeks when hopefully Mulgrew, Rodwell and Lenihan are fit.
"We came out of League One last year and I think we've done fantastically well. We were two points off the play-offs only six weeks ago."