James Norwood's 10th goal of the season saw Forest Green secure a league double over Hyde and remain fourth.
David Poole almost gave Hyde a third-minute lead but his shot came crashing back off the crossbar.
Norwood slotted into the far corner from just inside the area but was later denied twice by keeper David Carnell.
The Hyde keeper saved from Reece Styche late on, while Adam Griffin forced a save out of Sam Russell at the other end as Rovers secured the win.
VIEWS FROM THE DRESSING ROOM
Forest Green Rovers manager Dave Hockaday told BBC Radio Gloucestershire
"It's a brilliant three points, I can't tell you how happy and proud I am that we've got those points and kept another clean sheet.
"Hyde are a really good footballing team and we've come here and took them on, I thought we were the better team.
"We're starting to look as if we're enjoying this grind that we talk about.
"To win away at Newport and Hyde is a statement and we've got to keep it going."
Hyde 01 Carnell 02 Brizell (Cox - 83' Booked ) 03 Griffin 05 Ashworth 16 Lomax 07 Poole 15 Allott 17 Cassidy (Blinkhorn - 60' ) 21 Tomsett 09 Spencer 10 Jevons (Harris - 71' ) Substitutes 12 Frith 08 Byrne 11 Cox 20 Blinkhorn 25 Harris Forest Green Rovers 23 Russell 02 Hodgkiss 03 Stokes 15 Oshodi 21 Racine 04 Bangura 08 Klukowski 11 Forbes 14 Taylor 19 Rowe (Styche - 79' ) 20 Norwood Booked Substitutes 16 Asafu-Adjaye 07 Koroma 09 Styche 10 Vieira 17 Marsh
Ref: Seb Stockbridge