Christian Roberts took a free kick for Swindon, but blasted the ball high into the away fans on the Stratton Bank. Barry Corr also hit the bar.
Forest Green had a goal ruled out for off side shortly before the half time break, but Swindon still managed to take the 1-0 lead into half time.
Fleetwood made it 1-1 on 54 minutes with a close range shot after Swindon had failed to clear the ball away.
Then on 66 minutes Beesley then gave the local Blue Square Premier side the lead with a header making it 1-2.
The game was a bit like the Stevange FA Cup tie nearly 10 years ago with the non league side leading 2-1 in rain, and a heavy wind.
But on 69 minutes Swindon were level again after a free kick was crossed in and met with a header from captain Hasney Aljofree.
Blair Sturrock came on as a sub and soon scored the winner for Swindon on 88 minutes with a close range goal making it 3-2 to Swindon.
Overall a lucky win for Swindon. Forest Green did very well, and should have at least got a draw out of the game. They bought around 1,500 fans to the game making the total attendance 7,588 - the second highest gate of the season, and the highest for a FA Cup 2nd round tie this year.