The home side always had the edge in the battle of the Rovers, but had to rely on centre-half Rob Jones to grab the all-important goal in the 63rd minute.
Tranmere never really threatened in a first half in which chances were few and far between.
But Doncaster always forced the pace and Kyle Bennett and David Cotterill both went close in the first quarter of the game.
Tranmere's only moment of menace before the break was a glancing header from Jean-Louis Akpa Akpro, which sailed just wide although they made a bright start to the second half.
Akpa Akpro volleyed into the side-netting in the 50th minute before the home side took charge and the visitors inevitably cracked.
A free-kick on the left from David Cotterill was headed down by Jamie McCombe and Jones flicked out a boot to guide home his seventh goal of the season from close range.