Doncaster were dreadful in a scrappy first half and were seldom able to string more than a couple of passes together.
County played with more freedom than their nervous opponents and went close when Dean Leacock fired just wide following a 10th-minute corner.
The visitors snatched the lead in spectacular style in the 14th minute and managed to cling on in a frantic finish.
Alan Judge tapped a 25-yard free-kick to Joss Labadie, who fired home a stunning shot into the top corner.
Doncaster midfielder Dean Furman headed home 10 minutes later only to have his effort disallowed for offside and it was not until the second half that the home side managed to step up the pace.
and substitute Iain Hume both had angled shots cleared off the goalline in the closing stages and James Coppinger and Chris Brown had efforts blocked in a terrific goalmouth scramble.
But Rovers had left their effort too late.