The Millers had failed to beat the visitors in their previous 12 meetings on home soil, a miserable run stretching back to April 1969.
Early on it was Crewe that looked sharp and they took the lead in the tenth minute when Luke Varney was on hand fire home after Neil Cutler had parried a low shot from Nicky Maynard in to his path.
Despite the blow, United rallied with Delroy Facey shooting against the post, before they grabbed a leveller after 32 minutes.
Ritchie Partridge's cross fell into the path of Will Hoskins, who set up Eugen Bopp to fire a crisp shop past Ben Williams.
Nine minutes later the hosts went in front when the outstanding Partridge steered the ball home following Hoskins' sublime flick.
In first-half stoppage time, United went further ahead when Lee Williamson netted his fifth goal of the season from the spot after Michael Higdon's crazy handball.
Hoskins, who was terrific all afternoon, made it 4-1 in the 65th minute with a fine finish after a clever turn in the box and Partridge grabbed his second goal with a superb 20-yard shot which flew into the top corner of the net.
The only sour point for the hosts came late on when Bopp was dismissed after picking up his second yellow card.