Stephen Dobbie almost put Fleetwood into an early lead when he found himself unmarked, but headed straight at Crawley keeper Brian Jensen.
It was all Fleetwood in the early stages as a hesitant Jensen allowed Jamie Proctor to climb above the Crawley defence and nod over the crossbar from a dead-ball situation.
After a bright start from Fleetwood, Crawley began to find their feet, although it was the away side who still seemed to be creating the better chances.
Gareth Evans had a good opportunity to open the deadlock, but opted to shoot and force a Jensen save when instead a square pass to the unmarked Matty Blair would have surely provided the opening goal.
As the second-half began, Jensen continued to be tested as Fleetwood began to dominate.
On the 51st minute, Proctor was denied once again by the big Dane, who was adamant on keeping a clean sheet.
Despite the goal, Fleetwood refused to give up on an equaliser and almost got it when Proctor just failed to convert an Evans cross.
Graham Alexander's men will feel that they deserved at least a point, but Crawley managed to hold on for victory.