Two second half headed goals from former Town trialist Marvin Elliott ensured the Glovers left West Sussex empty handed.
Gary Johnson was forced into making one change to his starting eleven after Ben Nugent was ruled out with a hamstring injury. The Cardiff City loanee was replaced at centre back by Jakub Sokolik.
Crawley made three changes from their recent game against Preston North End. Former Glover Lewis Young started on the bench and former trialist Elliott started for the home side.
Town started brightly with half chances falling to Kieffer Moore and Ajay Leith-Smith with the first ten minutes.
The Glovers nearly opened the scoring on 12 minutes when Joel Grant twisted and turned his way into a shooting position before firing a shot at goal. The Jamican international’s effort beat Ashdown in the Crawley goal but he saw his shot bounce back off the base of the upright.
Town could have taken the lead just before the 20-minute mark when Ajay Leitch-Smith put Kieffer Moore through, but the big striker’s shot went over the bar whilst under pressure from defender Walsh.
That proved to be the last bit of action for the former Dorchester man as five minutes later he limped off to be replaced by Kevin Dawson.
The home side had keeper Ashdown to thank for keeping the scores level just before the half hour mark. A Nathan Ralph cross was well met by Grant, but the big shot stopper saved well to deny the front man.
At half time the Glovers made their second substitute with the first substitute Dawson being replaced by James Hayter.
After dominating the first half Town were second best at the start of the second half and fell behind ten minutes in to the second period.
Good build up on the wing saw Smith’s pin point cross on to the head of Elliott who rose highest at the back post to powerfully head home from close range.
Just three minutes later the former Bristol City man scored again with his head after a cross from the right wing. The midfielder showed great desire to meet the cross and powerfully head home past Kean.
Town could have found themselves 3-0 down moments later when McLeod raced clear of the Town defence only to find Kean quick off his line to save well with his feet.
In the dying moments Martin rose highest at the back post, but his header was well saved by keeper Ashdown and Sokolik's header towards goal was easily cleared to safety.