Doncaster only had themselves to blame for missed chances as Crewe ended their seven match unbeaten run with a hard-earned victory.
Rovers were outplayed in the first half as the visitors passed the ball and retained possession impressively after on-loan Finnish striker Lauri Dalla Valle had grabbed a goal on his debut after just five minutes.
The 21-year-old, on loan from Fulham, outpaced a square Rovers rear guard to latch on to a superb defence-splitting pass from Chuks Aneke and fire home off the near post. Rovers were fortunate not to be further behind minutes later when an attempted clearance from Tommy Spurr sailed goal wards and Gary Woods had to claw the ball off the line.
Woods did well to tip away a dipping shot from Abdul Osman in and saw a cracking effort from Byron Moore rocking just wide.
Doncaster never troubled visiting keeper Alan Martin in the first half although midfielder Paul Keegan should have equalised just before the interval when he dribbled through in fine style but then fired well wide of the target.
The home side suffered a blow when influential skipper Rob Jones went off with a head injury but they raised their game after the interval. Teenage left-back James Husband raced through to have a fierce angled shot parried but when Paul Keegan latched on to the rebound he fired against the crossbar. Robbie Blake had an effort smothered by keeper Martin and Iain Hune soon after.
But it was the visitors who struck when big striker Mathias Pogba headed home at the far post.
Doncaster Rovers: Woods, Quinn, Husband, Jones (Martis 27), Spurr, Syers (Blake 46), Keegan, Harper (Brown 75), Martin Woods, Hume, Paynter. Unused substitutes: Griffin, Michael Woods, Sullivan, Clingan.
Crewe Alexandra: Martin, Toothill, Davis, Ellis, Murphy, Pogba, Moore (West 46), Mellor, Osman, Aneke (Robertson 90), Dalla Valle. Unused substitutes: Dugdale, Turton, Ray, Daniels.
Referee: S Duncan (Newcastle Upon Tyne).