It was Vale's seventh away match without a victory and they never looked like ending the sequence in a patchy performance.
In fact, it looked as if they would be happy to settle for a point from the start as they slowed the game down and tried to frustrate Rovers' attempts at high-speed football.
Doncaster were the better side throughout, although they were not on top form themselves.
They set the pattern for a one-sided first-half when James Coppinger had a shot blocked in the first minute following good work by James O'Connor and Paul Heffernan.
The home side suffered a blow when top-scorer Heffernan limped off in the seventh minute following a tackle from behind.
But they pressed on undaunted and were unlucky not to make the breakthrough six minutes later when visiting keeper Joe Anyon made a fine save to keep out a header from Graeme Lee.
Anyon was by far the busier of the two keepers and he came to the rescue again to save from Paul Green and Mark Wilson later in the half.
He was beaten by another powerful header from Mark McCammon but was fortunate to see the ball rebound off the crossbar.
Doncaster stepped up the pace in the second half and were rewarded when Price headed home from close range four minutes after the interval after McCammon had headed across the face of the goal following good work from Green and Coppinger.
Vale looked more menacing following the introduction of lively substitute Malvin Kamara for Ross Gardner in the 64th minute.
Kamara set up a great chance for Danny Whitaker two minutes after coming on but, although he was unsighted, Rovers' on-loan former Scotland international keeper Neil Sullivan produced a brilliant finger-tip save to claw the ball to safety.
Kamara went close with a volley in the 77th minute and Michael Husbands had another effort comfortably saved by Sullivan in the closing stages.
But Doncaster finished worthy winners with McCammon going close to adding to the score in injury time.