About 90 firefighters from San Jose and Cal Fire were dispatched to the blaze, which was contained at about 11:45 a.m., Capt. Mary Gutierrez said.
The San Jose Fire Department turned the operation over to Cal Fire at about 3 p.m. to free up its companies to respond to incidents in the city, Gutierrez said.
A couple of people hitting balls at the club's driving range reported the fire at about 9:45 a.m.
Firefighters had trouble accessing the two-alarm blaze because of the hilly terrain and two live wires that were downed mid-slope, according to Gutierrez.
PG&E was called to secure the lines.
Firefighters laid about 400 to 500 feet of hose while helicopter crews dropped water on the fire, Gutierrez said.
No structures were threatened, but the driving range was closed so that fire vehicles could drive over it to reach the base of the hill where the fire was burning, she said.
"It's a very slow-moving grass fire, and we're finally getting some water on it," she said.
She said it was not immediately clear how the fire started, but that the downed wires might have been the cause.
A San Jose firefighter suffered minor injuries, and was taken to a hospital and released.