'I'm pretty overwhelmed,' said Harris, who pocketed $225,000 for the victory. 'I'm really proud of the way I played. It's been a long four years.'
Harris fired a 7-under 64 in the final round to get into the clubhouse at 11-under-par 202. Jenkins birdied his 17th hole and made par from the rough at 18 for a 2-under 69.
The pair returned to the par-4 closing hole for the playoff. Harris, who bogeyed the hole in both the second and third rounds, spilt the fairway with his drive, while Jenkins landed in the right rough.
Jenkins had all kinds of tree trouble with his second, but played a nice shot short of the green. Harris hit a sensational 6-iron 6 feet right of the flag.
Jenkins pitched his third almost 7 feet from the hole, then drained the par save to apply the pressure on Harris. The former amateur star calmly sank his birdie putt for the win.
'I played this hole twice today and bogeyed it both times so I felt like it owed me something,' said Harris. 'I visualized good shots and they came off just the way I looked at them.'
The playoff culminated a long day at the Red Course at Eisenhower Park on Sunday. Heavy rain forced the suspension of play on Saturday, so most of the field completed the second round on Sunday before the final round.
Jay Haas, who was looking for his fourth consecutive win on the Champions Tour, let one get away on Sunday. He missed a 4-foot birdie putt on 17, then could not birdie the last to get into the extra session.
He shot a 2-under 69 and tied for third with Gil Morgan, who also carded a 69 in the final round, and Andy Bean, who bogeyed the last to miss the playoff and shoot a 4-under 67. The group came in at 10-under-par 203.
Dana Quigley posted a 6-under 65 in the final round to come in sixth place at minus-9.
Harris flew out of the gate in Sunday's final round with birdies at two, three and six. He closed his front nine with a birdie at the ninth, but his play on the back nine is what got him to the winner's circle.
He birdied the 11th and 12th holes, but when his 20-footer at the par-3 13th found the bottom of the cup, he found himself tied for the lead with Bean.
Bean, who will have to wait for Champions Tour win No. 1, fell down the leaderboard when his approach shot at 13 plugged in a bunker. He made bogey, but got the shot back with a 4-foot birdie putt at the next hole.
Harris, playing several groups ahead, rolled in an 18-foot birdie putt at the 16th to stay one ahead of Bean. Bean dropped a shot at the 16th to fall two back, but tapped in a short birdie putt at the par-5 17th to get within one.
Harris came back to the field at 18. His drive found the fairway, but his approach sailed right of the green. Harris chipped his third to 35 feet and two-putted to fall back into a tie with Bean.
Bean was the next to tumble at the final hole. He drove into the right rough and his second landed short and left of the green. Bean hit his third 6 feet past the hole and missed the par putt, leaving Jenkins, Haas and Morgan as the only players who could tie Harris.
Haas birdied the 14th to get to minus-10, but could not get anything to fall the rest of the way. He had a 4-footer at 17, but pushed it.
Jenkins, who collected only one previous birdie at the seventh, rolled in a 4-footer of his own for a birdie at the 17th. Morgan holed an 18-footer at the same hole to get within one.
At the 18th, Jenkins was tied for the lead with Harris, while Morgan and Haas needed birdies to tie. Jenkins drove into the right rough and came up short of the putting surface with his second. Morgan never factored into the hole and Haas gave himself a 25-foot chance to reach 11 under par.
Jenkins chipped to 2 feet and kicked in the par putt. Haas missed his birdie try to leave Harris and Jenkins to the playoff.
Dave Eichelberger, Scott Simpson and Massy Kuramoto all carded rounds of 2- under 69 on Sunday. They tied for seventh place with Tom Wargo, who shot a 70 in the final round, at 8-under-par 205.