The playoff was necessitated when Wiebe and Mason both ended with 7-under 65s to finish at 19-under-par 197.
Both made birdie putts on the first playoff hole, after which came a weather delay. Play resumed an hour later and the pair again played No. 18 and again knotted, with both golfers making par.
That set up a third extra hole played on the par-3 No. 17 at the Rock Barn Golf & Spa.
Wiebe and Mason both hit the green with their first shots, with Wiebe much further away. His birdie try rolled 5 feet past the cup, while Mason's ran 4 feet past the hole.
Wiebe then converted for par, but Mason missed on the left edge, handing Wiebe his third career Champions Tour win.
Fred Funk carded a 10-under 62 for a share of third place with Chip Beck (66) at minus-18.