Rovers had to settle for a share of the points after being pegged back at Ewood Park.
Sam Gallagher's sensational 13th minute strike looked to have set Rovers on their way to successive home victories, until Dave Edwards headed home 12 minutes from time.
Both sides could have won the match in an open ending to the game, but a draw was just about the right result.
Rovers made two enforced changes for the tea-time clash at Ewood Park.
With injuries to Tommie Hoban and Derrick Williams, that meant a first home start for Charlie Mulgrew, whilst Gordon Greer returned to partner Darragh Lenihan in the centre of defence.
There were three changes to the Wolves starting eleven as Jed Wallace, Conor Coady and Cameron Borthwick-Jackson all came in for Silvia Sa Pereira, Nouha Dicko and Joao Teixeira.
Under the lights at Ewood the match was somewhat of a slow burner in the opening minutes, but it was sparked into life with a stunning opening goal for Rovers on 13.
Danny Guthrie spotted the overlapping run of Jason Lowe down the right and although his first centre was cut out, the Rovers captain showed great awareness to put the ball back into the centre to where Gallagher unleashed an unstoppable volley into the top corner of the net leaving Carl Ikeme grasping thin air.
Indeed Wolves could have had two goalkeepers and they still wouldn't have stopped it as the young striker celebrated his sixth goal of the season.
That prompted an immediate response from the visitors as they created a host of opportunities to put Rovers under a sustained spell of pressure.
Jon Dadi Bodvarsson and Jed Wallace both failed to test Jason Steele, then Edwards flicked narrowly wide, before Conor Coady fired over.
Wolves midfielder Coady was then denied by the legs of the Rovers' number one as Steele showed great reactions to a deflected strike from the edge of the box.
However it was the home side who ended the first half strongly. Greer headed over a Craig Conway free-kick. Then great hold up play by Gallagher saw him release Marshall who cut inside onto his right to let fly, but Ikeme at full stretch tipped the ball around the post.
That would prove to be Ikeme's last involvement as the keeper wouldn't return for the second half, Andy Lonergan on as his replacement.
Rovers pressured from the off and saw strong claims for a penalty waved away when Romain Saiss handled in the area, but home appeals went unheard.
Then from a Conway corner on the right the ball ran through to Lenihan at the back post, the Irishman struck it sweetly on the volley left-footed, but a Wolves boot blocked the shot in the six-yard box.
Rovers continued to maintain the forward momentum with a gilt-edge chance on 63 minutes. Marvin Emnes showed good trickery in the corner of the box to make space for the pass, he picked out strike-partner Gallagher who set himself before shooting, but Lonergan saved with his legs.
Despite that strong start to the second half, it was the visitors who slowly came back into the match. Edwards showing his danger as he headed over a Costa centre.
And with 12 minutes to go that pressure from Wolves eventually told, albeit in contentious circumstances.
Substitute Teixeira forced a fine save from Steele, but as Matt Doherty put the ball back into the area, Edwards looked to be at least a yard offside as he headed home the equaliser.
All square, the game could have gone either way in a end-to-end finish to the match.
Steele saved well to deny Ivan Cavaleiro, before Conway saw an effort kept out at the other end.
Sub Anthony Stokes then set up two chances in quick succession on 90 minutes, but neither Gallagher or fellow sub Stephen Hendrie could threaten the target as the match ended a goal a-piece.
ROVERS: Steele, Lowe, Lenihan, Greer, Mulgrew (sub Hendrie 72 mins), Marshall, Guthrie, Evans, Conway, Emnes (sub Stokes 80 mins), Gallagher.
Subs not used: Raya (GK), Feeney, Samuelsen, Akpan, Bennett.
Goals: Gallagher 13 mins.
Booked: Marshall 58 mins, Guthrie 75 mins.
WOLVES: Ikeme (sub Lonergan 46 mins), Doherty, Edwards, Batth (c), Wallace (sub Cavaleiro 65 mins), Coady, Costa, Dadi Bodvarsson, Saiss (sub Teixeira 56 mins), Borthwick-Jackson, Hause.
Subs not used: Sa Pereira, Stearman, Saville, Dicko.
Goals: Edwards 78 mins.
Booked: Batth 26 mins, Teixeira 64 mins.
Attendance: 10,652 (including 821 visiting supporters)