Rovers fell to a first home defeat to top six opposition this season, despite a valiant second-half performance. Aaron Collins' 46th minute strike set up a thrilling encounter after Wednesday had scored twice in the first half through Bannan and Famewo.
Rovers made three changes from Saturday's 1-1 draw with Derby County for the visit of Sheffield Wednesday. In came Loft, Coburn and Quansah, for Sinclair, Finley and Anderson, who all dropped to the bench.
Wednesday struck the bar early on from a Smith header, but the striker was flagged offside, before Lewis Gibson, newly-installed as captain, almost gifted the Owls the lead with a thirteenth-minute backpass that Smith almost intercepted.
Smith saw yellow on 15 for a late tackle on Gibson.
Rovers' first shot on target came in the 21st minute as Loft volleyed goalwards from a Hoole cross, but straight at Dawson.
Wednesday went ahead after 29 minutes as Barry Bannan picked up a loose Quansah pass and rifled home from thirty-yards beyond Belshaw into the bottom left corner of the net.
The Owls doubled their advantage after 41 minutes, when a loose ball from a corner was struck home from close range by Famewo.
Rovers won a corner as the half drew to a close, but the visitors cleared and the Gas went into the interval trailing by two goals to nil.
Rovers made three changes for the second half, with Evans, Finley and Sinclair replacing Connolly, Ward and Loft.
The impact was immediate as Collins sprinted through and finished under Dawson to halve the dedficit in the 46th minute.
Gibson made a crucial interception as Wednesday broke away, before play was stopped for an injury to Famewo. The goalscorer couldn't continue and was substituted, whilst Vaulks was booked for delaying the restart.
Sinclair nearly pounced on a clearance after 58 after a good ball from Evans had put Coburn in behind.
Coburn's drive from distance was deflected narrowly wide for a Rovers corner, but a foul on Flint relieved the pressure on the Owls.
Sinclair gave the ball away on 62 and Gregory played in Smith, but he couldn't keep his shot down.
Rovers continued to dominate possession but couldn't find a way through, so Marquis was introduced in place of Gordon to try and find the equaliser.
He so nearly scored with his first touch, but Hoole's cross was just glanced away from his head for a corner.
Marquis thought he'd equalised with ten minutes remaining as he tapped in Finley's shot, but the offside flag thwarted the celebrations.
Evans then curled narrowly wide from the edge of the box as Wednesday half-cleared a cross in the 82nd minute.
Joey Barton picked up a booking for questioning a foul given against Collins on the touchline, before Anderson replaced Bogarde. Wednesday defender Palmer was also booked for time-wasting.
Collins shot on target, but a deflection brought an injury-time corner for Rovers, but the visitors clung on.
Next up for Rovers is a trip to Port Vale on Saturday 22nd April for a Sky Bet League One game (kick-off 3pm).
ROVERS: Belshaw, Connolly (Evans 46), Gordon, Quansah, Gibson (c), Hoole, Ward (Finley 46), Bogarde, Loft (Sinclair 46), Collins, Coburn.
Subs: Ward, Finley, Sinclair, Marquis, Anderson, Evans, Gibbons.
WEDNESDAY: Dawson, Palmer, Vaulks, Iorfa, Adeniran, Gregory, Bannan (c), Famewo, Johnson, Smith, Flint.
Subs: Stockdale, Brown, Paterson, Dele-Bashiru, Bakinson, Shipston, Durrant.
Referee: Josh Smith