Nelson and Irwin returned to the par-5 18th tee for the extra session. Irwin, the all-time wins leader of the Champions Tour, knocked his second shot to the front edge of green.
Nelson, who won the FedEx Kinko's Classic earlier this year, found a greenside bunker with his second. He blasted to 5 feet. Irwin's eagle try came up well short and he left the birdie putt just short of the cup.
Before Irwin could kick in his par putt, Nelson drained his birdie try for win No. 2 this season and No. 19 of his career.
'I really wasn't thinking about winning as much as I was thinking about shooting as low as I could,' Nelson said. 'My goal was 20 Champions Tour victories. You don't know when your last one will be. This one was nice.'
Peter Jacobsen, who won the U.S. Senior Open earlier in the season, bogeyed the last to close with a 5-under 67. He shared third place with first-and second-round leader Wayne Levi at 13-under-par 203. Levi was trying to become the first player in Champions Tour history to win in wire-to-wire fashion two straight weeks.
Morris Hatalsky closed with a 68 to finish at 11-under-par 205. He was joined in fifth place by Jim Thorpe and Jim Dent, who each posted final-round 69s at Augusta Pines Golf Club.
Nelson began his day seven shots behind Levi and tied for 14th place. He quickly jumped into red figures with back-to-back birdies from the first. Nelson collected birdies at four and six to move to minus-10.
The 57-year-old stumbled to a bogey at the eighth. Nelson bounced back from that mistake with a birdie at the 10th. He dropped in a birdie at the 12th and came right back to birdie 13 to get to 12 under.
Nelson drained the eighth birdie of his round at the 15th. He came right back with a birdie at the par-4 16th to tie Jacobsen in the lead. Nelson tripped to another bogey at the 17 to fall one shot back.
Nelson fought back to birdie the par-5 closing hole to finish at minus-14.
'I really putted well today,' said Nelson, who picked up $240,000 for the win. 'The biggest putt I made was on 17. It was a looping putt. Every so often you get a gift and this was one of those.'
After his drive found water on 18, Jacobsen stumbled to a bogey to fall one behind Nelson.
Irwin birdied one and two, but faltered to a bogey at the third. He cruised around the turn with eight straight pars. He rolled in a birdie at the 12th to move to minus-11.
The 40-time winner on the Champions Tour then eagled the par-4 14th to get within one shot of the lead. He birdied the par-5 closing hole to join Nelson in the playoff. However, he could not come through in the playoff and finished second for the second straight week.
'I putted so poorly,' Irwin said. 'I had chances to end it at 16 and 17, but I missed short putts. I'm just not putting well. There is no way to sugar-coat it. As disappointing as the finish was, I've had two consecutive seconds.'
Des Smyth and David Eger each posted 4-under 68s in the final round to share eighth place with Mark Johnson and Tom Kite, who both shot 69, at 10-under-par 206.
Craig Stadler was trying to tie Chi Chi Rodriguez' Champions Tour record of four consecutive wins, but closed with back-to-back 71s to share 28th place at 5-under-par 211.