Tom Pope grabbed an early opener when the Gills were caught napping before Nicky Maynard wrapped up the points shortly into the second half.
Gillingham had Kevin Maher dismissed in the 58th minute for a dangerous tackle on Kenny Lunt before Dean Morgan added a third for Crewe.
The Gills now sit four points above the relegation zone, albeit with a game in hand over Steve Holland's men, but looked doomed to the drop on this evidence.
The visitors sounded a warning in the eighth minute with a Gary Roberts shot that flashed across the face of the Gillingham goal.
And a minute later the Railwaymen were celebrating after keeper Ben Williams scuffed a clearance straight to Morgan who found Maynard with a defence-splitting pass that the striker coolly lifted over Simon Royce into the net.
Gillingham failed to lift themselves, appearing clueless in attack, and on 37 minutes Maynard clipped the ball just past the far post from Michael O'Connor's pass.
Moments later Maynard struck the outside of the post from a difficult angle after beating Royce to Lunt's pass.
Gillingham came out with renewed vigour after the break and Adam Miller was unlucky to see his fierce shot cannon back off Williams' far post.
But just two minutes later, Crewe managed to break free through Roberts who found Maynard with a cross-cum-shot that the recalled striker crashed home from inside the six-yard box.
Any hopes of a Gillingham comeback were extinguished with Maher's dismissal just before the hour mark for a lunge on Lunt.
Skipper Andrew Crofts did go close to reducing the deficit with a close-range header on 67 minutes that brought a fantastic save out of Williams but, as the home side pushed forward, Tom Pope found Morgan with a precise throughball and the burly forward held off his marker before beating Royce with a low finish.