Teenage striker Nicky Maynard gave Crewe a dream start with a super goal in the 11th minute but the visitors were unable to maintain the momentum.
The opening minutes were scrappy, although Bruce Dyer had a low shot saved moments before Maynard pounced at the other end.
The 19-year-old celebrated his full debut for Alex when he ghosted inside from the left and curled an angled right-foot shot into the roof of the net to the delight of the away fans.
Maynard went close again with a deflected effort a couple of minutes later but it was virtually all Doncaster for the rest of the half. Jonathan Forte and James Coppinger went close to scoring before Dyer equalised following a slick passing move in the 19th minute.
The former Sheffield United striker latched onto a return pass from Paul Heffernan and hammered the ball low into the bottom corner from just inside the box.
Crewe's goal led a charmed life after that with Coppinger twice having efforts saved by Ben Williams while Heffernan was denied by a desperate last-ditch tackle.
Doncaster stepped up the pace in the second half and made the breakthrough in the 63rd minute when Kevin Horlock scored his first goal for the club following a great run from midfield.
Gareth Roberts and Forte combined to set up the chance with Horlock darting onto the winger's through ball to fire home from close range.
Forte hit a volley on the turn just wide and Maynard had a shot deflected following a rare attack at the other end before Rovers wrapped up the points.
Coppinger was rewarded for a fine display when he latched onto a pass from Dyer and wrong-footed the unsighted Williams with a low shot from the edge of the penalty area in the 71st minute.
Alan Blayney tipped a 25-yard free kick from David Vaughan over the bar when Crewe tried to hit back, but Rovers finished well on top with Coppinger close to adding a fourth four minutes from time.