Shrewsbury Town's first ever trip to the Keepmoat Stadium ended in defeat as Doncaster sealed victory with an early penalty
Billy Paynter fired home from the spot on just three minutes after Matt Richards brought down David Cotterill.
David Syers had the ball in the net seven minutes later for the hosts but the offside flag was already up.
Terry Gornell - who limped off with a knee injury on the half hour - had Town's only real first half chance when he headed a difficult opportunity wide from a cross from Marvin Morgan.
Shrewsbury were a far more significant threat after the break with Morgan missing the target with a 10-yard header and then seeing an effort from a tight angle tipped around the post by Doncaster goalkeeper Gary Woods.
Paul Parry and Jon Taylor also had headed chances while Woods was forced to be alert to make a save when a low Taylor cross was deflected towards goal by Tommy Spurr.
But, despite being the better side in the second half, there was no way back for Graham Turner's side.