The 58-year-old Haas made a 5-foot birdie putt on the par-5 18th after hitting his second shot into a greenside bunker and leaving his eagle blast short.
"It was just a very magical day for me," Haas said. "I had a great pairing. I love playing with Freddie. ... It was a wonderful day. One of those that you don't want to end."
Haas became the eighth player in the history of the 50-and-over tour to shoot 60, and the first since Nick Price last year in the Toshiba Classic.
"I can't remember another time that I've had a chance to shoot a 59," Haas said. "I was thinking about it without question. I hit a decent bunker shot. It stopped a little quicker for me than I thought."
Haas also broke the course record on Desert Mountain's Cochise layout, closing with a 7-under 28 on the back nine to finish a stroke off the tour's nine-hole record.
Tom Lehman was second in the season-ending event after a 63, moving into position to win the Charles Schwab Cup points race. Bernhard Langer, 211 points ahead of second-place Lehman, was tied for fifth at 6 under after a 65.
Couples was third at 8 under after a 66.
"Wow! What a round he had," Couples said about Haas. "I had a good time, 4-under par. I'm not going to complain, but when a guy is shooting 10 under it seems like you're shooting 80."
Haas is 14 under after two days in perfect conditions on the mountainside course. The nine-time PGA Tour winner won the Principal Charity Classic in Iowa in June for his 16th victory on the senior tour.
"The course is magnificent," Haas said. "The fairways are like carpets. The greens are perfect. So, if you hit a poor shot, it's my fault."
After making three birdies on the front nine to take the lead at 7 under, Haas chipped in for birdie from 35 feet on the par-4 10th after his 8-iron approach landed on the false front and spun off into the rough.
That was the only green he missed in regulation, and gave him a chance to test his work Monday with noted short-game instructor Stan Utley.
"I spent about an hour with Stan Utley up here at Grayhawk and he gave me some tips," Haas said. "I told him I was chipping really poorly, and he gave me some things to think about. ... I certainly have to applaud Stan for that."
He also birdied the next three holes, holing a 7-foot putt on No. 11 and 15-footers on 12 and 13.
"I kind of should have known my day was going really well because I thought I pushed the putt on 11," he said. "I started walking and I misread it. It broke a lot more than I thought and it caught the high edge and went into the hole."
Haas missed an 8-foot birdie try on the par-4 14th and settled for a birdie on the par-5 15th after missing a 9-foot eagle putt.
"Fifteen was the break of the day, really," Haas said. "I had too much club in my hand with 21-degree hybrid. Hit it in the neck just a little bit, and it hit just short and kicked up. ... I didn't hit it the way I wanted to, but it turned out nicely."
He parred the par-4 16th after a 117-yard wedge shot that came up 20 feet short and right, then hit a 5-iron to 8 feet to set up a birdie on the par-3 17th.
Couples is playing for the first time since a back injury forced him to withdraw during the first round of the Boeing Classic outside Seattle in late August. Before this week, he hadn't completed a competitive round since winning the Senior British Open in July for his second victory of the year.
"I'm excited to be out here playing," Couples said.
Lehman's 63 was his lowest round on the Champions Tour.
"I was extremely pleased with my play today," Lehman said. "As disappointed as I was with my finish yesterday, it was just the opposite today."
Langer and Lehman would win the season title with a victory, while third-place Roger Chapman needs a victory and some help to top the standings.
The tournament winner will get 880 points, with players receiving a point for every $500 they earn in the $2.5 million event.
Langer won the points title in 2010, and Lehman won last year.
"We're out there to do the best we can and at the end of the day we'll find out what happens," Langer said.
Chapman was tied for 21st in the 30-man field at 1 under after a 70.
Jay Don Blake, the defending champion and first-round leader, followed his opening 64 with a 71 to drop into a tie for eighth at 5 under. Blake won last year at TPC Harding Park in San Francisco.