Gary Alexander's late penalty rescued a point for promotion-chasing Crawley while Crewe remain in the hunt for a League Two play-off place.
Byron Moore's strike from 18 yards put Crewe - who are now two points behind Oxford United in seventh - in front.
Crawley keeper Michel Kuipers was in fine form preventing Moore twice while also denying Ajay Leitch-Smith.
Crewe looked to be heading for victory before Lee Bell handled Josh Taylor's cross to earn Crawley a penalty.
The result leaves Crawley in the top three, a point above Shrewsbury, who have a game in hand.
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Crawley manager Steve Evans told BBC Sussex:
"I think Crewe were the better side in the first half. We had one or two who decided to enjoy the occasion rather than play. We changed it at half-time, and from then on in it was them on the counter-attack and us dominating.
"The crowd were fantastic, and there is a great togetherness in the squad. We're here seeing ourselves against one of the best teams in the league in Crewe.
"We're depleted and they've got everybody. We're patching holes with square pegs, but we know why that is. It's because of the unprofessional behaviour of three others at Bradford."
Crewe manager Steve Davis told BBC Radio Stoke:
"In fairness we should have been out of sight because we totally dominated the first half and had numerous chances which we should have converted.
"They were always going to have a spell in the game in the second half, I felt that was coming but thought we defended it superbly well.
"It was very harsh and very cruel on us that we were unable to finish the game off because I thought that we deserved to.
"I know Steve Evans always talks about them being a good footballing side but he's seen a good footballing side today. He would have accepted being beaten."