A wonder strike in the 28th minute from Harry Cornick secured the three points for Paul Sturrock's men.
Manager Sturrock gave a debut to academy player Ollie Bassett and at the age of just 17, six months and 13 days he became the youngest player to play for Yeovil Town in the Football League.
The former youngest player to play for Yeovil in the football league was Steven Caulker, who was aged 6432 days old when played for Town against Tranmere Rovers - young Ollie beats the record by just 26 days.
Sturrock was forced to sit the stands to watch the match after being dismissed in the recent home match against Morecambe.
After a bright start by both teams it was the home side who had the first chance of the game when Darren Barnard connected to a deep cross, only to put his effort wide.
With 13 minutes on the clock a ball over the top from Jakub Sokolik was somehow sliced by Crawley defender Jon Ashton into the path of Ryan Bird, but the strikers effort went wide of Woodman’s goal.
Three minutes later the home side had keeper Woodman to thank for keeping the score at 0-0. Cornick latched onto a poor header back from Ashton, and with just Woodman to beat the on loan Bournemouth man’s effort was saved by the feet of the shot stopper to save Ashton’s blushes.
Just before the half hour mark Town took the lead thanks to an unstoppable shot from Cornick. The loanee picked up a pass from Dolan, he then cut in from the left wing to unleash a shot that left Woodman with no chance as it nestled into the top corner of the net.
One minute into the second half and the home side should have leveled the scores. A free kick on the right was swung in by Rooney and found its way to Bradley at the back post, but somehow the big defender put his shot wide with the goal at his mercy.
On the hour mark Bradley again went close for the home side when his bullet header cannoned back off the cross bar after a pin-point corner from Rooney.
Seconds later debutant Bassett found himself in room just inside the Crawley area, but the youngster scuffed his shot and the home side managed to clear away any danger.
With 83 minutes on the clock Cornick robbed Ashton on the half way to run clear of the Crawley back line, but with Scales covering well the goalscorer could only fire his shot at Woodman.