The 36-year-old Californian, runner-up in this competition in 1992, was landing his second career victory, and the pounds 300,000 top prize marked the biggest pay-day of his 14-year career.
Waldorf fired a par-71 final round to match Paulson at eight-under par 276 after 72 holes. Paulson shot a final-round 67 at the pounds 1.65m event to set up the eighth play-off here in the past 14 years.
Waldorf, whose previous win was at the 1995 La Cantera Open, lost his only previous PGA play-off in 1997 at Williamsburg to give world number one David Duval his first title.
The second round co-leader Chris Perry finished alone in third place at 277 while Scott Hoch had a 69 to finish fourth. The two-time champion Vijay Singh of Fiji, Doug Barron, Loren Roberts, Jim Carter and Sweden's Gabriel Hjertstedt shared fifth.
"I never thought I could make six bogeys in a round and still be in the tournament. I've never, ever had a finish where I was able to come back from behind and win," said Waldorf.
Paulson said: "The way Duffy came through with birdies on 17 and 18, I take my hat off to him, that was really impressive. It's not like this was a tournament where we were 22 under par, we were just eight under for the whole week, and he had two of those shots in the last two holes."
Hale Irwin fired a closing round of 65 to secure a seven-stroke victory in the Senior Players Championship at Dearborn in Michigan.
Irwin's seven-under-par effort gave him a 21-under total of 267, which matched the lowest winning score in the event since it moved to the current Jack Nicklaus-designed TPC of Michigan venue in 1991.
It was the 54-year-old American's fifth PGA seniors major crown as he beat Australia's Graham Marsh, who closed with a 68, into a distant second place, with John Jacobs (67) eight strokes off the pace in third.
Scores, Digest, page 25