Town never managed to land a single shot on target, but their defence was more than a match for a Rovers attack missing several key players.
Rovers lacked the goal punch of top-scorer Paul Heffernan and the power of Mark McCammon and they were also without skilful winger James Coppinger and on-loan wing-back Alan Wright.
Yeovil never looked like taking advantage of a depleted Rovers squad despite making a bright start.
On-loan midfielder Nicky Law sprayed the ball about effectively and Jean-Paul Kalala worked tremendously hard alongside him.
But, just like Doncaster, the final ball was lacking once they closed in on goal.
Rovers looked more dangerous once they settled into their stride and Jason Price had an angle shot well saved by visiting keeper Steve Mildenhall following good work by Paul Green in the 23rd minute.
Jonathan Forte cleverly put Lewis Guy through a couple of minutes later but his shot was deflected off a defender when he should have done better.
Doncaster came closest to breaking the deadlock just before the interval when skipper Graeme Lee was twice denied in the space of a minute.
Lee had a volley cleared off the line following a free-kick from Brian Stock and then was foiled by Mildenhall from point-blank range from the resulting corner.
Both sides did their best to attack in the second half but defences continued to remain on top with Lee and Adam Lockwood in tremendous form for Rovers.
Terry Skiverton and Terrell Forbes were just as commanding at the heart of the visitors' defence and the result was a stalemate.
It needed a tremendous block tackle from left-back Nathan Jones to prevent Price from hitting the target in the 66th minute, but the longer the game went on, the less likely it seemed that either side would score.
The last chance came deep into injury time when Lee nodded down a free-kick from Stock but Green was unable to put sufficient power behind his close-range shot and Mildenhall saved comfortably.