Grant McCann's side produced a perfect away performance at Gresty Road with goals in either half from Luke Molyneux and Harrison Biggins.
Rovers rode out some early pressure from the hosts, with Thimothee Lo-Tutala required to make a couple of saves as Crewe went in search of an early opener.
But once they had seen off those half-chances they took the lead against the run of play on 34 minutes. Hakeeb Adelakun and Matty Craig worked it well down the left before the latter picked out Molyneux who fired home from just outside the six-yard box. Biggins then came within a whisker of a quickfire second only to see his sidefooted attempt kiss the crossbar.
But Biggins made amends just after the restart, tapping home Joe Ironside's centre after he pounced on a defensive slip from Crewe's Mickey Demetriou.
And that's how it stayed although the visitors probed to try and extend their buffer ahead of Friday's return tie in South Yorkshire.
Here's how we rated the players.
But once they had seen off those half-chances they took the lead against the run of play on 34 minutes. Hakeeb Adelakun and Matty Craig worked it well down the left before the latter picked out Molyneux who fired home from just outside the six-yard box. Biggins then came within a whisker of a quickfire second only to see his sidefooted attempt kiss the crossbar.
![Got forward and linked up well with Adelakun down the left flank. Put in a great, last-ditch slide tackle second half to snub out a dangerous Crewe attack. Was superb going forward.](https://www.doncasterfreepress.co.uk/webimg/b25lY21zOjdkMzZiNDFkLWVmZDctNDZmMC1hNzNiLTk4YTZkZWQyMzc2YzpmMjQyZGYwZC05ZWZmLTQ5NGUtOTBkYS1mMTMwNGQyYWYzNjY=.jpg?crop=3:2&trim=&width=640)
5. James Maxwell 8
Got forward and linked up well with Adelakun down the left flank. Put in a great, last-ditch slide tackle second half to snub out a dangerous Crewe attack. Was superb going forward.Photo: Howard Roe/AHPIX LTD
![We shouldn't really expect anything else from him should we? Hard-working, covered almost every blade of grass.](https://www.doncasterfreepress.co.uk/webimg/b25lY21zOjYwYTIzNGY2LTM4YjctNDA5Ny1iNjliLTZmMmYzMDExODRmYjpmMzg0NDEwOS1kMTgyLTRiNTItYjUyNS1jNWFiMTEyOGU3ZTg=.jpg?crop=3:2&trim=&width=640)
6. Owen Bailey 8
We shouldn't really expect anything else from him should we? Hard-working, covered almost every blade of grass.Photo: Howard Roe/AHPIX LTD
![The Spurs loanee provided a classy pick-out for Molyneux but contributed so much more. Was scintillating. Punchy passes and tough in the tackle, he's destined for a future much higher up the pyramid - but hopefully still plenty to give Rovers before the season's out.](https://www.doncasterfreepress.co.uk/webimg/b25lY21zOmEyOTU0MDI4LWYwNjItNDM5My04N2M5LWFlNDA3NTAzMjgyMTo4MGVjN2E2ZS0xNjJlLTQ3YjgtYmQ3Yy03NzRkYjg1MWEzNDI=.jpg?crop=3:2&trim=&width=640)
7. Matty Craig 9
The Spurs loanee provided a classy pick-out for Molyneux but contributed so much more. Was scintillating. Punchy passes and tough in the tackle, he's destined for a future much higher up the pyramid - but hopefully still plenty to give Rovers before the season's out.Photo: Andrew Roe/AHPIX LTD
![Was busy and energetic on his return to the side. Slammed a sidefooter against the crossbar first half but went one better just after the restart with a tidy finish from Ironside's centre. Went off injured straight after the goal.](https://www.doncasterfreepress.co.uk/webimg/b25lY21zOjJjNjM3YjQwLWI2YjktNGM2ZS05N2YzLWE0OTE0ZGEyYmNkNzo2MmVhZTEyNy1jZjYxLTQ5YzctYjc5ZC01MTUzMjkzZDZjNzU=.jpg?crop=3:2&trim=&width=640)
8. Harrison Biggins 8
Was busy and energetic on his return to the side. Slammed a sidefooter against the crossbar first half but went one better just after the restart with a tidy finish from Ironside's centre. Went off injured straight after the goal.Photo: Howard Roe/AHPIX LTD