Crawley started the brighter in what proved a poor first half.
In Gwion Edwards they had a lively midfield influence and in Lewis Young they had a man willing to harry Fleetwood down the left flank.
But for all their early pressure the visitors couldn’t really find a way to test Chris Maxwell in the Fleetwood goal.
Even when the hosts invited the Red Devils forward they couldn’t take advantage, Edwards driving through the middle but frustrated by a last minute Mark Roberts block.
Crawley gradually retreated, choosing to sit deep and try to use the pace of Young on the break.
It was a strategy which played into Fleetwood’s hands, only the host’s poor touch around the box keeping Crawley keeper Lewis Price out of work.
Antoni Sarcevic looked the danger man, twice pulling efforts out of the hat which did draw saves from Price.
The second, a stinging volley from 10 yards could have produced an opener, Price diving to tip over when he looked beaten.
Sarcevic deserved a reward and got it before the break.
Former Crawley man Jamie Proctor took an elbow from Marvin Elliott as he tracked across the 18 yard line.
Up stepped Sarcevic, drilling a free kick under wall and keeper, a poor goal for Crawley to concede at the end of a poor half.
The home side could have doubled their advantage within minutes of the restart, Jeff Hughes getting a clean head on a Josh Morris corner but unable to guide it under the bar.
But Crawley came back into it, forcing the issue and taking more advantage of a nervous home side.
A second from Sarcevic might have settled the nerves, the midfielder beating Price to a long ball over the top, his lob coming back off the woodwork.
Proctor could have settled matters with four minutes remaining winning the ball in central midfield and charging into the box, his shot just tipped wide by Price.