Stephen Dawson put an effort over the bar from 20 yards early on for Rochdale before Done put the visitors in front with a powerful finish from outside the box.
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From the resulting corner, Harrold headed across goal to present a great chance for Sonny Bradley, but he could only hit the ball over the bar.
The dangerous Harrold then had another header denied by Logan as Crawley looked to get back into the game.
They did little to help themselves, however, and they were caught napping by Bastien Hery from a Rochdale throw as he sent an effort past the upright from the edge of the area.
A ten-minute spell then saw Vincenti take the game out of Crawley's reach with two well-taken goals.
Firstly, the midfielder calmly finished past Jensen from 12 yards before heading home a dinked cross from close range.
Andrew added a fourth for Rochdale to seal an impressive win for the visitors.