Despite Adam Le Fondre's missed penalty in the second half, an own goal from Adam Dugdale gave Rotherham the spoils.
Dugdale turned the ball past Rhys Taylor from close range under pressure from Mark Bradley after just 2 minutes for the only goal of the afternoon, but how it stayed that way was remarkable.
Marcus Marshall was the main threat for the Millers as his pace wide right caused problems for Crewe's back line.
Ryan Taylor had a shot smartly saved and his header crashed off the bar in an enterprising first half which also saw Shaun Miller, former Rotherham player Dave Artell and Clayton Donaldson go close for the Alex.
After the break the Millers continued to press and Kevin Ellison had a shot saved on the angle after being released by Marshall, and moments later Nicky Law's tricky play saw his cross flash across the Crewe six yard line.
Dugdale almost made up for his own goal on his home debut but his 25 yard rocket whizzed over Jamie Annerson's bar before the Millers had a chance to extend their lead from the spot.
Pat Ada's handball was penalised but Le Fondre's spot kick was tipped onto the post by Taylor to deny the forward a 17th goal of the season.
However it wasn't to prove costly as the Millers finished as they had started the afternoon.
Law fired a shot over in the closing stages and Ryan Taylor again had an effort saved as Crewe somehow kept the scoreline down to just one.