Chesterfield ended a run of six successive league defeats with late goals from Kristian Dennis and Jordan Flores giving them their first points under new manager Jack Lester.
The Spireites' first win since August 19 sent Crawley down to their sixth defeat in seven home league games this season.
Chesterfield came close to taking the lead after only five minutes when, after a flowing move, defender Bradley Barry had a goal-bound shot blocked by defender Joe McNerney.
Crawley midfielder Jordan Roberts had a free kick easily saved by keeper Joe Anyon before Chesterfield defender Andy Kellett forced a smart save from Glenn Morris.
Barry forced Morris to make another low save after Crawley defender McNerney had a close range header comfortably taken by keeper Anyon.
Morris showed alertness again by saving a goal-bound shot from Kristian Dennis after Crawley skipper Jimmy Smith had a shot blocked at the other end.
Crawley, with only two home league wins since mid January, struggled to impose themselves although Billy Clifford had a shot saved low down on the hour.
The hosts threatened eight minutes later when, after Enzio Boldewijn was brought down, a Roberts free kick was parried by keeper Anyon.
Flores had a left-foot shot parried by Morris before Chesterfield broke the deadlock on 73 minutes when Dennis scored his eighth goal of the season from close range after a cross from Flores.
Flores made the points safe two minutes from time by firing into the bottom corner from just outside the area.