League Two leaders Swindon suffered only their second league defeat of 2012 as goals from Nick Powell and Ashley Westwood gave Crewe the victory.
Powell scored his fifth goal in six games with a shot from the edge of the area, which went in off the crossbar.
Westwood doubled Alex's lead when he finished off a well-worked team goal with an angled effort from six yards.
Swindon's Ronan Murray missed a one-on-one, Simon Ferry hit the post and Paul Benson's effort also hit the woodwork.
The Robins' lead at the top of the table has been reduced to four points, while Crewe remain ninth, three points off a play-off place.
VIEWS FROM THE DRESSING ROOM
Crewe manager Steve Davis:
"It was a fantastic effort from the players. We started the game at a really high tempo and I think we caught them out with it.
"They couldn't really settle in to the game because we unsettled them with our pressure, and went on to create three or four good chances.
"I thought our back four performed excellently under a lot of pressure in the second half, and it was a great clean sheet for us."
Swindon Town manager Paolo di Canio told BBC Wiltshire:
"For me it was simply ridiculous. We deserved to lose.
"Today the fault is (with) Paolo di Canio because probably I lost in the last few weeks my humility.
"Some of my players lost some humility, passion, desire. I don't want to burn what we have built. I have to discover why.
"Today they behaved as stupid and silly lads."