The result leaves Wrexham in third position in League Two with five games of their season remaining.
Wrexham have a two-point advantage over fourth-placed MK Dons but have a game in hand in the battle for automatic promotion.
But an Owen Bailey goal a minute before half-time at the Eco-Power Stadium was enough to secure a fifth straight victory for a Doncaster team that moved up to 14th place.
Paul Mullin had the ball in the net for what would have been his 100th goal for Wrexham in the 77th minute but the flag went up to rule it out for offside.
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