The result means the Shrews, League One play-off finalists last season, remain in the bottom three whilst Doncaster stay in the top six.
Rovers bossed the early stages and Joe Wright glanced a header narrowly wide.
Shrewsbury looked to have been denied a clear penalty on 18 minutes when Shaun Whalley was stopped in his tracks by Doncaster’s Andy Butler but referee Darren Drysdale waved play on.
Down the other end Shrewsbury keeper Joel Coleman was kept busy, first keeping out Tommy Rowe’s fierce shot before denying the lively Mallik Wilks.
The restart saw Rovers come out bustling with energy but it was the visitors who looked dangerous on the counter.
Lenell John-Lewis was kept out twice by Marko Marosi before Greg Docherty forced a smart save from the home keeper.
John Marquis almost stole a win for the hosts late on but narrowly nodded past a post.