Rotherham remain top of League Two with a third win of the season despite some ambitious attacking play by Crewe.
Adam Le Fondre put Rotherham in front, against the run of play, when he headed in Lewis Grabban's cross.
After the break, Millers substitute Ben Pringle's deflected shot beat Alex keeper Steve Phillips.
Byron Moore drilled Shaun Miller's pass into the bottom corner to give Crewe hope but, despite a hatful of chances, the hosts could not draw level.
VIEWS FROM THE DRESSING ROOM
Crewe manager Dario Gradi told BBC Radio Stoke:
"We made two mistakes that they didn't make and that was the difference.
"I can't go in and criticise them, they're down enough. However much anybody else feels it, they feel it the worst.
"Every game is an opportunity to change the fortune. We could just do with a bit of luck."
Rotherham boss Andy Scott told BBC Radio Sheffield:
"Sometimes in this league you've got to come away from home and you've got to graft and be solid, organised and prepared to put your body on the line and not play great but get a result.
"sometimes if you're not playing great, things go against you, if you buckle it shows a sign of weakness. We haven't got that, we're organised, we're strong and we're prepared to battle for each, and they enjoy doing that"
"I'm proud of every one of the team, its been a tough start to the season, everyone thought it was a tough start, and sometimes scruffy wins are good."