Jack Ross men will have the chance to close the gap when they host relegation-threatened Walsall at the Stadium of Light on Saturday afternoon (3pm kick-off).
Despite dominating possession in the second half, it could have been worse for Barnsley after goalkeeper Adam Davies made an impressive save to deny Kieran Sadlier late on.
Barnsley were still without winger Jacob Brown and midfielder Cameron McGeehan who were serving the final matches of the three-game suspensions.
Sunderland handed promotion boost after Barnsley draw vs Doncaster
The Tykes also lost defensive midfielder Kenny Dougall to injury in the first half, with Zeki Fryers taking his place on 18 minutes.
The result marked a sixth successive clean sheet for Barnsley in League One, yet they now need Sunderland or Luton to drop points to secure a top-two spot.
After the Walsall game Sunderland wont play another league fixture until April 4, due to international call-ups and the Checkatrade Trophy final.
In that time Barnsley will make the trip to Walsall next weekend before hosting Coventry at the end of March.
Grant McCanns side tired after the break but held firm after coming under increasing pressure from the Reds.
In the end a draw was a fair result which kept both sides hopes of promotion ticking over – leaving second-placed Barnsley five points clear of Sunderland and edging Rovers, in sixth, two points ahead of nearest challengers Peterborough United.
Rovers were desperate to end a run of five games without a win in the league but found their rivals, who extended their unbeaten run in League One to 18 games, a tough nut to crack.
However, if they can repeat this level of performance – and in particular the energy they showed in the first period – during the last nine games they will not finish far from sixth spot.
Mamadou Thiam fired into the side-netting within the opening minute but Rovers, who were snapping into tackles early on and winning more loose balls, made the brighter opening and went on to boss the first period – but could not make it count on the scoresheet.
Twice left back Danny Andrew produced excellent balls into the box. Firstly Wilks powerful header was saved by Adam Davies who then blocked Marquiss attempt on the rebound, before Wilks clever volley drifted just wide.
Rovers were slicker in possession and when Marquis played in the lively Wilks midway through the first period the Leeds United loanee should have made Davies work harder.
Doncasters tenacity and industry restricted the visitors to the occasional counter attack. Matty Blair had to produce an excellent covering tackle to stop Ben Williams in his tracks and Marko Marosi made a good save to deny Jordan Williams from converting a cross at the back post.
But it was Rovers who looked the more likely and, sandwiched between those two scares, they again went close when Andrews deep corner was pinged towards goal by James Coppinger but blocked again by Davies.
Rovers began the second period in a similar vein, winning the ball back in good areas and not giving the Reds time on the ball.
The pattern of the game was familiar too. The hosts were more fluent on the ball but Barnsley still carried a threat on the break.