Reid raised both hands and let out a deep sigh before humbly removing his cap and shaking Cooks hand at Crosswater Golf Club in central Oregon.
I just dont feel deserving, he said. But Im so grateful.
Reids two majors ' he also won the 2005 Senior PGA Championship ' are his only two wins on the tour.
Reid shot a final-round 70 and Cook had a 69 to finish at 16-under 272.
Cook, who was two strokes behind leader Brad Bryant going into the Sundays round, birdied the par-3 No. 17 hole to take a one-stroke lead to the final hole. But he hit into the bunker, settling for a bogey and forcing the playoff with Reid, who made par on the hole.
I didnt play like a champion, Cook said.
Bryant, who opened with a career-best 62, stumbled to a final-round 73 to wrap up with a 14-under 274. His opening round matched Doug Tewells record set in 2001 and matched by Tom Watson in 2003.
Reid joins Peter Jacobsen as having two Champions Tour victories in majors. The Provo, Utah, resident won twice on the PGA Tour.
Reid had not finished within the top 10 this year. His best finish was in a group at 12th at the Principal Charity Classic in West Des Moines, Iowa.
Cooks best finish this season was a tie for third at the Legends of Golf tournament in Savannah, Georgia. Bryants best was fourth at the Dicks Sporting Goods Open in June.
Larry Mize shot a 69 Sunday to finish at 13 under.
Defending champion Fred Funk was in a group tied for fifth with a final-round 69 for an 11-under 277. His three-shot victory over Mike Goodes last year was his first win in a major on the tour.
Funk was coming off a victory at the U.S. Senior Open, where he became the first player in a USGA championship to finish at 20-under par. A week earlier, he lost in a three-way playoff at the Senior British Open.
He also finished in the top 10 in the previous three Champions Tour majors this season, and remained in the lead for the Charles Schwab Cup.
Watson and Loren Roberts also finished at 11 under.
Watson had one of the biggest galleries on the 7,337-yard course built in the shadow of Mount Bachelor. He has said this week that hes met many well-wishers in the past month after losing in a playoff to Stewart Cink at the British Open.