Rovers started brightly and took the lead after 19 minutes when Marsh-Brown converted a cross by Liam Noble, the midfielder making his debut following suspension after a summer move from Notts County.
Woking tried to force their way back into the match before half-time but forward Zak Ansah saw his effort saved by Sam Russell.
The visitors were forced into a change after 30 minutes when midfielder Rob Sinclair was replaced by Darren Carter and then had a header from Noble ruled out for offside.
Woking defender Jake Caprice fired a long-range effort over before Noble's free-kick was saved and substitute Matt Tubbs was denied a second Rovers goal in stoppage time by another decent stop from Cardinals keeper Michael Poke.
Report supplied by the Press Association.
Match ends, Woking 0, Forest Green Rovers 1.
Second Half ends, Woking 0, Forest Green Rovers 1.
Substitution, Forest Green Rovers. Kieffer Moore replaces Christian Doidge.
Substitution, Woking. Max Kretzschmar replaces Fabio Saraiva.
Substitution, Woking. Anthony Edgar replaces Gozie Ugwu.
Substitution, Woking. Charlie Penny replaces Dennon Lewis.
Gozie Ugwu (Woking) is shown the yellow card for a bad foul.
Substitution, Forest Green Rovers. Matt Tubbs replaces Rhys Murphy.
Ben Jefford (Forest Green Rovers) is shown the yellow card for a bad foul.
Second Half begins Woking 0, Forest Green Rovers 1.
First Half ends, Woking 0, Forest Green Rovers 1.
Substitution, Forest Green Rovers. Darren Carter replaces Rob Sinclair.
Goal!  Woking 0, Forest Green Rovers 1. Keanu Marsh-Brown (Forest Green Rovers).
First Half begins.
Lineups are announced and players are warming up.
A first-half goal from Keanu Marsh-Brown proved enough to give Forest Green Rovers a 1-0 win at Woking.