Second-half efforts from Tamika Mkandawire and Adam Boyd secured a comfortable win for the O's at a restless Gresty Road, where protests against first-team coach Steve Holland continued.
Crewe were fortunate to see Sam Parkin's headed finish ruled out for a foul on keeper Steve Collis after 15 minutes.
And the big loan striker was always a threat to Crewe's brittle defence along with speedy winger Jason Demetriou.
A poor first half burst into life ten minutes before the break when O's keeper Glenn Morris denied Crewe's on-loan midfielder Stuart Green.
Then Collis did well to palm a Boyd strike away from the far corner.
Tom Pope toe-poked an effort wide and Green skied a half-chance for the home side.
But Alex were caught out in the 55th minute when Sean Thornton was given time to size up a pass for the unmarked Mkandawire to take the ball on into the box and fire under Collis.
Crewe's Michael O'Connor looked to have been felled by Stephen Purches as he broke clear, but play was waved on.
And Orient threatened to kill the game on the break with Demetriou blazing wide.
But Boyd effectively sealed the three points with 16 minutes left when he was allowed to cut in and deliver a thumping 25-yarder into the top corner.
Thornton went close with late efforts, but Crewe should at least have reduced the arrears.
Joel Grant, though, skied over with the goal at his mercy and substitute Shaun Miller saw his header saved at point-blank range by Morris.