The 50-year-old Toledo, making his ninth start on the 50-and-over tour, eagled the opening hole and finished with a 5-under 67 to match Goodes and Gene Sauers at 6-under 210 at The Woodlands Country Club.
Cinco de Mayo marks the Battle of Puebla on May 5, 1862, when Mexican troops defeated a French army of Napoleon III, then considered the mightiest military in the world.
"It's a special day for me," Toledo said. "It's a holiday and it's just winning on that day is the most incredible thing I've ever done, because winning on the Champions Tour, it's hard. I have dreams and goals in my life that I was going to win on the Champions Tour, and I think I'm going to keep winning. I believe in myself that I can go up there and win again and again and again."
Toledo gave a lot of credit to caddie Larry Dittman.
"Yeah, Larry Dittman really helped me in the playoff to stay focused on the game and kept telling me to finish your swing," Toledo said. "Obviously, I've been working with my coach but my caddie really, really got me in the game."
Goodes shot a 72, and Sauers — eliminated on the second playoff hole with a double bogey— had a 74.
Toledo, seven strokes behind Sauers entering the round, earned $270,000 for his second victory in a PGA Tour-sanctioned event. He also won the Web.com Tour's 2005 Lake Erie Charity Classic.
"I felt great this morning," Toledo said. "I told my wife that I was going to go out and shoot a 66 and
catch up with them. And I shoot 67. I guess that was good enough, but I was very focused on the game all day long."
The three players parred the first extra hole on the par-4 18th. Sauers dropped out on the second playoff hole — also on the 18th — after hitting his second shot into the water behind the green.
Toledo and Goodes went to the par-4 17th, and Toledo won with a tap-in par after Goodes missed a 5-footer.
"I played really good today," Goodes said. "I made four bogeys and never hit a bad shot."
Sauers had a triple bogey on the par-5 15th, the easiest hole in the tournament and one that he birdied in the first two rounds.
"I hit a bad chip shot and three-putted," Sauers said. "I gave the greens a little too much respect, thinking they were really fast, gave them too much respect and left it way short."
The three-time PGA Tour winner rebounded with a birdie on the par-3 16th to regain a share of the lead.
Toledo had a chance to pull ahead on the final hole, but his 20-foot birdie putt curved away at the last instant.
Mark Calcavecchia and Loren Roberts tied for fourth at 3 under. Calcavecchia shot 69, and Roberts had a 72.
Bernhard Langer kept the top spot in the Charles Schwab Cup points race. He closed with a 72 to tie for 25th at 5 over. Fred Funk, the 2012 winner, also finished 5 over after a 70.
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