Andrade two-putted from the back fringe on the par-5 18th, holing a 2 1/2-footer for his third victory of the year on the 50-and-over tour.
''I was thinking when I was driving to the 18th tee that, 'Bernhard won the Schwab Cup, he doesn't need to win this tournament as well. Maybe it should be my turn,''' Andrade said.
The 51-year-old Andrade shot a 6-under 64 on Desert Mountain's Cochise Course, making a 10-foot birdie putt on 18 to post at 14-under 266.
''I had to make that putt,'' Andrade said. ''It was a heck of a putt. It was a great putt.''
Langer missed a chance to win in regulation when his 18-foot eagle putt lipped out. He finished with a 67, then failed to get up and down for birdie from the right greenside rough in the playoff.
''I don't know how that ball stayed out, but it did,'' Langer said. ''In the playoff I hit a good tee shot, I thought, but it must have kicked left a little bit and got behind that one tree that sticks out, so I had to aim right and hit a big hook and it only drew a little bit. Then I ended up with a pretty nasty lie in the rough, so the chip went a little strong.''
The 58-year-old German star won the Charles Schwab Cup points title for the second straight year and record third time overall, earning a $1 million annuity. He easily beat Colin Montgomerie and Jeff Maggert after entering the week third in the standings.
''Obviously, my goal was to win the overall Schwab Cup, this trophy here, coming into this tournament,'' Langer said.
With players receiving a point for every $500 in the $2.5 million tournament, Langer earned 508 points with his $254,000 check to beat Montgomerie by 338 points and Maggert by 377.
Langer also won the money title for the record fourth straight year and record seventh time in eight years, finishing with $2,340,288. The two-time Masters champion won the Byron Nelson Award for the second straight year and fourth time overall as the tour's scoring leader.
''He's 58 and he's still the best that we have and he's a very dedicated player,'' Andrade said. ''I just look up to him. He's a Hall of Famer, he's a classy man and I'm just honored to be in his company and to be competing against him.''
Montgomerie and Maggert tied for 14th at 4 under, with each earning $52,000. Maggert shot 66, and Montgomerie 67. Montgomerie received a $500,000 annuity, and Maggert a $300,000 annuity.
Andrade earned $440,000 and a $200,000 annuity for his fourth-place finish in the standings. The four-time PGA Tour winner also teamed with Joe Durant - his playing partner Sunday - to win the Legends of Golf in April and won the Boeing Classic in August.
''Having Joe Durant as my partner today was huge,'' Andrade said.
Andrade bogeyed the par-5 15th after his approach went over the green and into a crevice, forcing him to take an unplayable lie.
''I'm in the middle of the fairway at 15 with a very easy 89 yards with a 56-degree sand wedge and I just kind of nerved out,'' Andrade said.
He got a big break on the par-3 17th when his tee shot went long, struck a rock and ricocheted onto the green to set up a two-putt par.
''I was really hoping to try to make that putt, that would really be awesome,'' Andrade said. ''Off the rocks, make the putt and maybe not seal the deal, but have a better chance. Those things have to happen for you to win and sometimes you get bad breaks, you hit a good shot and it turns out bad. ... So you've got to get a little lucky, everyone knows that. It was a fortunate break for me there.''
Andrade had a hole-in-one in his opening 65 and followed with rounds of 67 and 70 to begin the day four strokes behind third-round leader Michael Allen.
Allen finished third at 12 under after a 70. The Scottsdale resident took a one-stroke lead over Langer into the day after leading by six strokes midway through the third round.