Toledo made a 4-foot par putt at the 17th hole after Andrade's 6-foot par try lipped out. Toledo has won three of his four PGA Tour Champions titles in playoffs, and each has come on the third hole.
"Being in a playoff isn't easy," said Toledo, who shot 68 to finish at 11-under 205 on The Old Course. "There's a lot of stress and a lot of nerves. Sometimes I surprise myself how well I play in tough conditions."
Andrade (67) was looking for his fourth victory on the 50-and-older circuit in the last 10 months, but he bogeyed the 16th hole and missed a 5-foot birdie putt on the 18th hole in regulation.
"I just hit a very poor putt," Andrade said. "I probably hit the worst putt I've hit in quite a while. I got a little quick. I was thinking about winning instead of thinking about making the putt."
It looked like Andrade was going to lose on the first playoff hole when his second shot landed in the palmetto bushes, but he saved par. They each parred the 18th hole again before Andrade missed the 17th green with a pitching wedge from the fairway. Andrade's birdie chip almost went in but rolled past the hole.
Toledo, a former professional boxer, threw a punch to celebrate after his par putt disappeared.
"I throw a left hook," Toledo said. "Chi Chi (Rodriguez) has his thing; I have my thing. I'm a boxer, not a golfer."
It was the fourth playoff in the last seven years at the Allianz Championship.
Tom Lehman could have made it a three-way playoff, but he failed to birdie the par-5 18th, which played the easiest on the course (4.47). A bogey dropped Lehman (72) into fifth place.
"Everything that could go wrong went wrong on the last hole," Lehman said. "But it was a very tough day to play. Very pleased with the way I played."
Second-round leader Corey Pavin extended his advantage to two shots on the front nine but made six bogeys and faded to 10th after a 75. Pavin has just one victory in 112 starts on the PGA Tour Champions, and that came at the 2012 Allianz Championship.