Paul Lambert's Rovers had to settle for a point after twice being pegged back at Ewood.
Hope Akpan's first goal for the club put the home side in front early on, and although Modou Sougou levelled for the Owls, a Corry Evans strike saw Rovers lead at the break.
In a game of few chances, Rovers looked to be heading towards back-to-back wins for the first time this season, but with Grant Hanley stricken in the opposition box the visitors raced up the other end to score late on as substitute Lucas Joao headed home.
Jordan Rhodes could have snatched all three points with virtually the last kick of the game, but his header was saved to ensure the match ended all square.
For his first game in charge at Ewood Park Paul Lambert made just the one change from the side that had defeated Preston seven days earlier.
Chris Taylor was the man introduced, replacing Tom Lawrence who had suffered a kick on the calf at Deepdale.
It was a typical Lancashire welcome for Lambert with heavy rain and a swirling wind, but the noise from the home fans showed their support for the Scot.
On five minutes their efforts were rewarded when Rovers took the lead from their first attack. Craig Conway sending a corner into the area and Hope Akpan rose the highest to power the ball home.
The Nigerian international wheeled away in delight as he celebrated his first goal in a blue and white shirt.
Solid and compact, Rovers restricted the opposition to very little, whilst chances were few and far between at the other end.
So it was somewhat of a surprise when the Owls levelled on 39 minutes. Kieran Lee's run into the area went unchecked and as his shot struck the post, Sougou snapped up the rebound.
But it was Rovers who would go into the break with their noses in front with a goal right on half-time.
Again it was Conway with the assist as although his corner from the right was cleared as far as the edge of the box, Evans struck through the packed area with the ball deflecting into the back of the net.
Carlos Carvalhal made a double change at the break as Lucas Joao and Gary Hooper were introduced. Scot Hooper poking a shot wide when well placed after Joao's header deflected into his path.
Roared on by a home crowd as relentless as the rain it looked as though Rovers were going to be able to see the match out but six minutes from time the visitors grabbed an equaliser.
With Hanley down in the opposition penalty area, the Owls broke forward, Joao applying the finishing touch after the ball fell kindly for him in the area.
The closing stages saw Rovers look to claim the lead for a third time, but with the last chance of the game, a cross found Rhodes in the area, but his header was straight at Kieren Westwood to ensure the match ended all square.
ROVERS: Steele, Henley, Duffy, Hanley (c) (sub Henry 87 mins), Olsson, Marshall (sub Lawrence 90+3 mins), Evans, Akpan, Conway (sub Guthrie 78 mins), Taylor, Rhodes.
Subs not used: Eastwood (GK), Spurr, Delfouneso, Brown.
Goals: Akpan 5 mins, Evans 44 mins.
SHEFF WED: Westwood, Palmer, Loovens (c), Semedo, Nuhiu (sub Joao 46 mins), Lees, Helan (sub Hooper 46 mins), Lee, Sougou (sub Wallace 69 mins), Pudil, Forestieri.
Subs not used: Wildsmith (GK), McGugan, Dielna, Lopez.
Goals: Sougou 39 mins, Joao 84 mins.
Booked: Helan, Lee.
Attendance: 15,837 (including 3407 visiting supporters)