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.
"The chills were flying up and down," Kelly said. "It was pretty amazing. My mom saying the sun came out, my dad was there. I haven't won since my dad passed, so this was the first one and I was talking to him all the time. There were a lot of birdies coming up and chirping right next to me and I was like, `Hey, hey, Dad, how are you?' It was kind of surreal."
Goosen also had a 66, and Stricker shot 67.
"The playoff was exciting stuff," Goosen said. "It was good to be in that sort of fight again. It's been a while since I've been in that kind of position and it's nice to finally get in that position. Now we can grow on that and I'm looking forward to the U.S. (Senior) Open next week."
Stricker was eliminated with a bogey on the first extra hole. He missed an 8-foot birdie putt on the par-4 18th in regulation.
"I had some opportunities coming in at 15, 16, 18," Stricker said. "Pretty cautious with some of the putts. Didn't hit some of my best putts. Then had the opportunity to win it all right there on 18. Misread it a little bit. I didn't think it was going to break as much as it did and it just snapped off at the end."
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.
"It really is truly awesome," Kelly said. "It's about friends and family and to be able to do it in front of everybody ... this is pretty sweet."
Duffy Waldorf was a stroke out of the playoff after a 68.
Hall of Fame pitcher John Smoltz tied for 76th in the 78-man field at 12 over with rounds of 76, 78 and 74. Making his third tour start, the former Atlanta Braves star got into the field on a sponsor exemption.