Rovers slipped to a narrow 1-0 loss in a tough encounter at Ewood Park.
Steven Fletcher's deflected first half strike proved to be the difference in a tight match between two improving teams.
After Ben Marshall had stung the gloves of Keiren Westwood, the only goal of the came on 22 minutes when Fletcher hit a shot that clipped off a Rovers boot and gave Jason Steele no chance.
Another long-range strike saw Barry Bannan clip the top of the woodwork, but Marvin Emnes mis-kicked in front of goal on the stroke of half-time.
It was tougher going in the second half with few opportunities, but Rovers thought they had levelled ten minutes from time when Emnes fired home. However home celebrations were cut short by the linesman's flag much to the surprise of everyone in blue and white.
Unchanged for the third consecutive match, Rovers started confidently against an Owls side that had won three out of their last four games.
With both teams patient in possession it wasn't until the 21st minute that the first meaningful opening was created.
It came Rovers' way following an excellent tackle by Jason Lowe on Gary Hooper, that released Marshall on the attack but his stinging shot was turned behind by Keiren Westwood.
Wednesday's response saw them take the lead the very next minute. Out of nothing Fletcher collected a pass from Barry Bannan before hitting shot from outside the box flew off a Rovers ban and into the top corner of the net giving Jason Steele no chance.
No strangers to going behind, Rovers continued with their pressing play and neat interchange of passing. Only a last-ditch challenge from Sam Hutchinson prevented Sam Gallagher from getting in on goal.
But at the other end Fletcher fancied another. Full of confidence following his earlier strike, the Scottish international took a touch inside before letting fly from fully 30-yards, Steele at full stretch as the ball whistled beyond the far post.
A lovely piece of control from Marvin Emnes then set up Lowe for a cross, but Gallagher was just over with his header, before Liam Palmer saw a strike across the box deflect wide for the visitors.
The chances kept on coming as the opening half drew to a close. Barry Bannan clipped the corner of post and bar with a stunning long-range strike. But the home side's best chance came on 45 when Gallagher nodded down for Emnes, but the Dutchman mis-kicked in front of goal.
Like the first, the second half was slow to get going with only an ambitious strike from Will Buckley to show in the opening stages.
Rovers made their first change on 56 with Danny Graham replacing Sam Gallagher, before Darragh Lenihan was introduced as Danny Guthrie made way as the home side looked for a way to get back on level terms.
But they found it tough going against a well-drilled and hard-working Wednesday side. The front four, so potent in Saturday's win over Derby County, had little in the way of goalmouth opportunities.
Liam Feeney replaced Lowe as the home side made their final change with 13 minutes to go, but it was the visitors who posed more of a threat on the counter.
Yet after Steele had kept out a close range shot from Kieran Lee, Rovers thought they levelled with ten minutes to go. Lenihan drilled a ball across the box, it came out to Emnes, but as he blasted high into the roof of the net from ten yards, his celebrations were cut short by the flag of the linesman on the near side.
It seemed a perfectly good goal, the official spotting something that no-one else did.
Urged on by the home fans Rovers looked for one last sight of goal, but they were unable to breach a resolute Wednesday back line as the visitors held on for the victory.
ROVERS: Steele, Lowe (sub Feeney 77 mins), Greer, Hoban, Williams, Marshall, Guthrie, Evans, Conway, Emnes, Gallagher (sub Graham 57 mins).
Subs not used: Raya (GK), Samuelsen, Akpan, Lenihan, Brown.
SHEFF WED: Westwood, Jones, Lee, Fletcher (sub Nuhiu 81 mins), Reach, Hooper (sub Forestieri 73 mins), Lees (c), Palmer, Hutchinson (sub Loovens 61 mins), Buckley, Bannan.
Subs not used: Dawson, Abdi, Hunt, Wallace.
Goals: Fletcher 22 mins.
Attendance: 12,844 (including 2752 visiting supporters).