The 59-year-old Elliott, from West Des Moines, Iowa, won for the first time in 36 starts in USGA events. He also won the Senior British Amateur this summer at Ganton Golf Club in England.
The 58-year-old Gunthorpe, from Ovid, Michigan, never trailed until he missed an 8-foot par putt on 18.
“That match was so tough that I am not sure, did I win?” Elliott said. “I guess it just hasn’t sunk in yet. Just so much goes with that USGA title that maybe that’s why I haven’t won it in the past. It’s just so important and so meaningful to win a USGA championship. I’m relieved. I’m very proud. I didn’t do it by myself. I had a lot of help from a lot of different people, so it is a team win, really.”