The woman, who was not identified, was critically injured Sunday after plunging about 45 feet at O.co Coliseum. She jumped shortly after the Raiders' 23-19 loss to the Tennessee Titans, as fans filed out of the stadium.
The good Samaritan was seriously injured but was conscious and talking at the hospital, police said.
"He saved her life quite honestly, at his own expense," Alameda County Sheriff's Sgt. J.D. Nelson told the Oakland Tribune. "This guy 100 percent saved her life. She'd be dead now."
Nelson said the woman went to a seating area that was covered by a tarp and appeared to be alone when she jumped. Fans who spotted her tried to stop her.
"I yelled at her, 'Don't do it, please don't do it!' about 10 times. But she crawled out to the edge and jumped," witness Ron Brown of Sacramento told KTVU-TV.
The injured man was with a friend lingering near the flagpoles and Al Davis commemorative flame when he saw the commotion around the woman, Nelson told KTVU-TV.
The man also repeatedly shouted, "Don't do it," as he lunged toward the woman as she dropped and was knocked down as he tried to catch her, Nelson said.
Arriving paramedics found the woman in very critical condition, and the man also injured on the concourse. Initially, they thought she fell on him, but witnesses say he actually jumped to where she was falling, and tried to save her.
Nelson visited the injured man in the hospital Sunday evening.
"He just couldn't imagine having people see that," Nelson said. "He said it was a reaction. Even now, at the hospital he's very concerned about her. He's a real compassionate person."
The 61-year-old man's name was not released. Nelson told the TV station the man is from Stockton, had served in the Marine Corps, is a longtime Raiders fan and a season ticket holder.
On the NFL's opening day this year, a fan died from a fall off a pedestrian overpass outside Candlestick Park in San Francisco, and two others were injured when a railing collapsed at the Colts game against the Raiders in Indianapolis.