Two strokes behind Pavin after 10 holes in the final round, the 50-year-old Couples played the final eight in 7 under, making an eagle — his second of the round — and five birdies.
"I don't know if I putted like that on the PGA Tour, ever," said Couples, who had only 24 putts in the final round. "I used to putt well and once you hit your mid-40s, every putt is important."
The former University of Houston star finished at 17-under 199 on The Woodlands Country Club course and earned $255,000 for his fourth Champions Tour victory of the year.
Mark Wiebe (71) was second, Dan Forsman (66) and Brad Bryant (66) followed at 9 under, and Pavin (74) and John Cook (67) tied for fifth at 8 under.
Couples birdied Nos. 11 and 12 to tie Pavin, then made a long eagle putt on the par-5 13th. After Couples' eagle, Pavin made a bogey, missing a 7-foot putt.
"That was something," Couples said. "I played well yesterday and I felt I'd play well today. I assumed one of us (in lead threesome) would win. To be honest, I hit the ball well and made a lot of putts and it all added up to a 63."
Couples moved two more shots ahead on the next hole with another birdie and Pavin's bogey.
Couples also birdied Nos. 16 and 18.
"Fred played great, it was a pretty amazing nine holes," Pavin said. "It was tough to keep up with him. I wasn't playing well anyway. I was out in front of the ball today. I struggled all day and it never turned around. ... Things weren't clicking, I'll try again next week. I haven't played much golf lately, only the second event since Oregon. I hope to compete the next two weeks. It would be nice to get a win."
Bernhard Langer, 535 points ahead of second-place Couples in the Charles Schwab Cup standings, shot a 66 to tie for 13th at 3 under. Kenny Perry tied for 35th in his first start on the 50-and-over tour, closing with a 70 to finish at 1 over.
Couples is skipping the AT&T Championship this week in San Antonio.
"I'd have to say it is important, but I physically couldn't play next week," Couples said. "I'm exhausted. If I played next week, I wouldn't be ready for the Schwab Cup.
"I physically couldn't play next week I'm drained. I'd get a couple of days off and then have to play in the Wednesday pro-am and the Thursday pro-am."