Rovers' best moments came courtesy of midfielder John Spicer, who shot just wide early in the second half, and Martin Woods, but they struggled for fluency and created very few chances as on-loan striker Billy Sharp was deprived of quality service.
Rovers were without suspended midfielders John Oster and Quinton Fortune, who were sent-off in the derby draw with Scunthorpe.
Spicer, James Hayter and Dean Shiels came into the side while James Coppinger missed out after failing to recover from calf problems.
The visitors were without Dutch midfielder Ferrie Bodde, who will miss the rest of the season after suffering a second serious knee injury in 10 months.
Nathan Dyer and Jordi Lopez were suspended following their red cards in the weekend's 2-1 win over Sheffield United so Thomas Butler, Marcos Painter and Ashley Richards were named in the starting XI, with Beattie claiming a place in attack.
The visitors made a bright start and created the first clear-cut chance as Beattie headed over when winger Mark Gower's corner found him unmarked at the near post.
Rovers replied with a surging attack that saw Angel Rangel earn a booking for bringing down Martin Woods, who forced a superb save from Dorus De Vries from the resulting free-kick before Shiels dragged a long-range effort wide of the left-hand post during a lively opening 10 minutes.
The Swans then wasted the first of three gilt-edged chances to take the lead after 23 minutes.
Butler's superb cross was missed altogether by Gorka Pintado with the goal at his mercy, and moments later the Spanish forward's excellent run and pull-back saw Beattie shoot straight at Neil Sullivan in the Doncaster goal.
The treble of misses was completed when Butler headed against the underside of the bar from another Gower corner.
Shiels saw his volley deflected over the bar by Rangel as Sean O'Driscoll's side rallied but the visitors continued to look the more incisive of the two sides.
The lively Spicer almost made Paolo Sousa's men pay for their missed chances as he slalomed past three defenders from the restart to place a shot just wide of De Vries' right-hand post.
But that was to be as close as the hosts got to a goal as they struggled to break down Swansea with countless passes going astray in the final third.
Gower's low free-kick into the area somehow evaded everyone while Mark Wilson fired wide for Doncaster as the game became increasingly scrappy.
Woods forced De Vries into parrying his free-kick, after Ashley Williams' handball, and substitute Stephen Dobbie, on for Beattie, blazed over from distance for the Welsh side as a disappointing second half drew to a close on a night that would have done little to cheer either manager.