Tranmere edged the first half but overall the home side did most of the attacking, with skilful winger James Coppinger causing problems with his tricky play on the right.
But the visitors remained resolute throughout with commanding central defender Ian Goodison a tower of strength at the back.
Experienced strikers Gareth Taylor and Chris Greenacre won their fare share of the aerial battles and they combined to set up a chance for Chris Shuker, who hammered a low 20-yarder just wide in the seventh minute.
John Mullin had a low shot comfortably saved by Alan Blayney a minute later before Doncaster began to make their prescience felt.
Tranmere skipper Shane Sherriff had to head behind for a corner when Graeme Lee threatened and then Gavin Ward saved bravely at the feet of Adam Lockwood following a goalmouth scramble.
Defences stayed on top with clear-cut chances few and far between although Sean Thornton had a 20-yard shot saved and Greenacre had a header deflected at the other end.
Doncaster stepped up the pace in the second half with Paul Heffernan having a shot deflected into the hands of Ward, before Thornton sent over a corner from which Lee had a header saved.
The best chance of the match fell to Heffernan following brilliant work by Coppinger in the 57th minute, but the Irish striker headed wide in front of goal.
Tranmere's best scoring opportunity came three minutes later when Kevin Ellison blasted wide after Greenacre supplied the cross.
Tranmere had to defend in the closing stages as Doncaster pushed more and more players forward, but the home side were unable to make the breakthrough.
Big substitute Mark McCammon had a header saved from Jason Price's right-wing cross in the 73rd minute and Thornton had a fierce 20-yard shot parried by Ward three minutes later.
Lee struck a volley which was deflected fractionally wide in the 89th minute and Coppinger sent a terrific 30-yarder dipping just over the bar as Doncaster tried to snatch victory.