Sylvan Ebanks-Blake's shot hit both posts before going in, then Lee Novak doubled the home lead on 12 minutes, side-footing in from six yards.
Callum Saunders went close before Zoumana Bakayogo replied for Crewe, scoring from Brad Inman's cut-back.
Connor Dimaio sealed Chesterfield's win just before the hour following a neat one-two with Ebanks-Blake.
Chesterfield's first victory in six games lifts them to 19th in the table, one point clear of the relegation zone and six above second-from-bottom Crewe, who suffered a first defeat in seven games.
Crewe manager Steve Davis told BBC Radio Stoke:
"Now we have to go again. We have been on a great little run. We'd have liked to have won one or two of them along the way but it has shown what we are capable of.
"We played some terrific football at times and had enough chances to have got something. I thought the better team lost.
"What we didn't do well was defend. We gave them gifts for the goals and those individual errors have proved costly. The full-back slipped for the first. then we didn't pick up at the far post properly and, for the third one, we didn't track the runner."
Two early goals gave Chesterfield the initiative as they won the battle of League One strugglers against Crewe.