Ronan Darcy gave the Reds an early lead but Callum Morton’s first half double claimed all three points for Rovers.
The defeat sees Scott Lindsey’s side drop to 14th in the table, while victory for Rovers has moved them out of the relegation places.
Crawley remained unchanged from Tuesday evening’s draw at Walsall, with Liam Kelly once again captaining the side in Ben Gladwin’s absence.
The Reds needed just six minutes to go ahead in an enthralling first 45 minutes. Darcy received the ball inside the area and powered his effort into the far corner to make it 1-0 Crawley.
The visitors should have doubled their advantage just four minutes later. Nick Tsaroulla raced through on goal but goalkeeper James Belshaw – who was outstanding for Rovers – stood tall to keep out the 24-year-old.
Forest Green had a golden opportunity to level on 15 minutes. Morton drilled a ball into the box which flicked up onto the head of ex-Watford hero Troy Deeney, but he could only head wide.
A perfectly executed Crawley set-piece routine fell to Klaidi Lolos in the area, but Belshaw saved well again.
But the first half momentum swung in Rovers’ favour on 27 minutes. Harvey Bunker threaded a pass through to Morton, who cut in on his right foot and fired past Reds stopper Corey Addai.
Forest Green were just inches away from taking the lead moments later. Kyle McAllister took aim from the edge of the box but his shot deflected just wide.
Rovers took the lead on the stroke of half-time. A mix-up in the Crawley defence allowed Morton to grab his second of the afternoon, and turn the game on its head.
The Reds started the second period brightly but were met with firm resistance by Belshaw. Darcy forced a save from the Forest Green goalkeeper after dispossessing a defender, before the Bristol Rovers loanee reacted brilliantly to keep out Will Wright's shot from inside the box.
Lolos was then denied from close-range with his back to goal, and Addai made himself big to thwart Jamie Robson as both teams exchanged blows.
Tsaroulla then danced into the Rovers box but Callum Jones made an inch-perfect tackle just as the Crawley fan favourite was about to pull the trigger.
Forest Green had two chances to add a third in the game’s dying embers. Deeney met a cross at the far post, but his header bounced into the ground and on to the roof of the net. Mathew Stevens then made his way into the Reds area from outside the box and forced a terrific diving save from Addai.
Crawley Town: Addai, Wright, Johnson (Henry 73), Maguire, Gordon (Forster 81), Darcy (Roles 81), Williams, Kelly, Tsaroulla, Orsi, Lolos.
Unused: Ashby-Hammond, Omole, Swyer, Khaleel.