Kelly closed with a 6-under 66 at rainy University Ridge to match Goosen and tournament host and fellow Madison player Steve Stricker at 15-under 201. Goosen also had a 66, and Stricker shot 67.
Stricker was eliminated with a bogey on the first extra hole. He missed a short birdie putt on the par-4 18th in regulation.
Kelly won on the par-4 15th after the playoff opened with two trips down the 18th. Kelly has four victories on the 50-and-over tour after winning three times on the PGA Tour.
Duffy Waldorf was a stroke out of the playoff after a 68.