Lewis Holtby bagged a first half brace as Rovers produced arguably their best performance of the season to earn a biggest league win since October 2001.
It was a confident start to proceedings for the visitors, with Holtby scoring from close range midway through the half before Massimo Luongo was shown a straight red for a challenge on Lewis Travis.
The visitors didn't let up, with an own goal from Cameron Dawson arriving prior to Holtby's close range finish making it 3-0 before the break.
Darragh Lenihan made it four just after the interval and there were only seconds remaining of the encounter when Sam Gallagher made it a fantastic five late on.
That ensured Rovers registered their biggest win since beating West Ham United 7-1 19 years ago.
The one change made by Tony Mowbray saw Corry Evans drop out due to a long-term injury and was replaced by Joe Rothwell.
Evans' omission saw Stewart Downing move from his usual wing position to take a place alongside Travis in central midfield.
Rovers had the better of the early stages in the Steel City and good play involving Gallagher and the returning Rothwell led to the winger's cross being cut out before reaching the advanced Holtby.
Holtby was involved in the opener soon after as he tucked home from close range after Adam Armstrong nodded the ball down into his path.
The move started with Tosin Adarabioyo's pass that took out the home midfield, and after Armstrong's strike was beaten back into his path by Cameron Dawson, the forward made no mistake in setting up his team-mate.
At the other end, Jacob Murphy's left-footed shot was comfortable for Christian Walton to hold onto down low to his left.
More drama arrived a moment or two later when Luongo was shown a straight red card for a stamping challenge of Lewis Travis.
There was no doubt in referee Jarred Gillett's mind in sending off his Australian compatriot midway through the first half, with Wednesday having to play the remainder of the encounter a man light.
Things got better for Rovers with nine minutes to go until the break as more fortune went the way of Mowbray's men in achieving a second of the afternoon.
Ryan Nyambe put the hard yards in down the right and found Travis, and although the midfielder's effort was brilliantly tipped onto the post by Dawson, the ball hit the home 'keeper on the back and trickled in.
A stunning first half performance was complete just seconds before the half time whistle when Holtby bagged his second of the game.
Armstrong was the tormentor, found a way past home debutant Osaze Urhoghide and set up the playmaker to tap home from a couple of yards to complete a 45 minutes where the visitors simply ran riot.
Owls boss Garry Monk made two changes for the beginning of the second half with Kieran Lee and Urhoghide being replaced by Sam Hutchinson and Tom Lees.
There was almost a fourth of the day for Rovers just a minute after the break, but only a superb save from Dawson prevented Adam Reach from scoring an own goal after fine work from Rothwell down the left flank.
But that goal did arrived from the resulting corner as Stewart Downing's outswinging set piece was met by Lenihan, who marked his 150th Rovers appearance with a first strike on the road in blue-and-white for the Irishman.
Rovers confidently stroked the ball around and it took until the final 20 minutes for the next opportunity to arrive for Mowbray's side.
Good work from Gallagher down the right saw him skip past Morgan Fox and unleash a shot that Dawson was forced to tip behind for a corner.
The fifth goal was there for Rovers if they wanted it and Armstrong went close to getting his name on the scoresheet when he drove towards goal, but Dawson managed to deny the 22-year-old.
Joe Rankin-Costello was on for his first team league debut early in the second half and he went close to marking the occasion with a goal with ten minutes remaining, but his strike from the edge of the box flew just past the post.
There was still time for Gallagher to add a fifth in added time, latching onto a threaded pass from Rankin-Costello and connected with a strike that flew past Dawson and into the roof of the net.
That was the crowning moment on a sensational team display, with Rovers set up for our next game - at home to Queens Park Rangers - very nicely.
Sheffield Wednesday: Dawson, Fox, Lee (Hutchinson, 46), Bannan (c), Winnall, Borner, Murphy, Reach, Luongo, Iorfa, Urhoghide (Lees, 46).
Unused substitutes: Wildsmith, Rhodes, Harris, Pelupessy.
Booked: Borner, 14
Sent off: Luongo, 23
Rovers: Walton, Nyambe, Lenihan (c), Adarabioyo, Bell, Travis (Davenport, 72), Downing, Armstrong (Brereton, 87), Holtby, Rothwell (Rankin-Costello, 59), Gallagher.
Unused substitutes: Leutwiler, Williams, Graham, Bennett.
Goal: Holtby, 19, 45, Dawson OG, 36, Lenihan, 48, Gallagher, 90.
Booked: Rothwell, 56.
Referee: Jarred Gillett.