Armour, who won the event for the third time in its 43-year history, had a final-round 67 for a 14-under 274. He began the day trailing Janzen, the two-time U.S. Open champion, by two shots.
The co-leader after three rounds with Andrew Putnam, Janzen finished with a 69.
After hitting his tee shot on the 18th hole of regulation onto the beach, Armour recovered with a 17-foot birdie putt to match Janzen at 14 under.
Janzen had just made a 30-foot birdie from the front fringe.
"When I saw the ball on the beach I knew there was no other way," said Armour, the 2007 and 2008 winner who used a 7-iron to get back on the fairway. "I've had that shot before but I've never made it."
Janzen, who joined the Champions Tour in August, held a two-shot lead at 15 under after 12 holes. But Janzen, whose last PGA Tour win was the 1998 U.S. Open, then bogeyed twice, while Armour made five straight pars through the 17th.
"I chunked a wedge on 13 and made bogey and that was the start of it," said Janzen. "I hit some bad shots and some good shoots and there were some good things to build on."
Janzen and Armour both hit their playoff-hole tee shots on the 18th behind trees. Both players hit low second shots with Janzen's effort hitting Armour's ball in the fairway.
Armour hit his third shot past the hole and it rolled back. Janzen missed an estimated 15-footer birdie before Armour's winning putt.
Kevin Sutherland, the 2000 winner of the tournament that featured 83 pros from the four major tours as well as mini tour players and club pros, finished alone in third at 10 under after a 67.
Mina Harigae, the LPGA veteran who was the only woman to make the cut, finished with a 76 and at 4 over 292.