Bryant padded his lead to go 15 under after three rounds at Crosswater Golf Club in central Oregon. He has stayed atop the leaderboard after shooting a career-best 10-under 62 in the opening round, matching a tournament record.
Reid birdied the par-4 No. 18 to finish with a 66 and go to 13 under in the fourth of five majors on the Champions Tour.
Bryant had back-to-back birdies on the 15th and 16th holes. He came close to another one on the par-3 No. 17, but his putt came to rest on the lip of the hole.
"Definitely could have been a little more tidy today," Cook said. "But I'm happy with that."
Bryant's best finish of the year was fourth at the Dick's Sporting Goods Open in June, and he has four overall Tour victories, his last coming at the Senior U.S. Open in 2007.
Reid has just one win on the Champions Tour, the 2005 Senior PGA Championship.
Watson rebounded with a 69 on Saturday after a 74 the day before, but making a run at the leaders in the final round would be tough at 6 under.
Watson had one of the biggest galleries on the 7,533-yard course built in the shadow of Mount Bachelor. He has said this week that he's encountered many well-wishers in the past month, after losing in a playoff to Stewart Cink at the British Open.
After temperatures nearly hit 100 on Thursday, a cooling trend expected to continue through the weekend brought highs into the mid-80s.
Funk had a 73 Saturday and was 8 under after three rounds.