Schauffele had a 17-under 193 total at TPC River Highlands. Cantlay shot 63.
Schauffele began the day at 14 under with a 5-stroke lead. The Olympic champion birdied the second hole for the third time this week and had another at No. 6, part of a career-best run of 48 holes without a bogey.
But he put his tee shot at 13 in the water and briefly fell into a tie for the lead after a bogey. He broke his minor birdie drought at 16 then hit the pin on his approach at 17 and sank another.
"I would love to have that tee ball back on 13," he said. "For the most part, I knew it wasn't going to be easy to protect a lead, especially when it's 5 shots and it's easy to get comfortable."
Cantlay's bogey-free round was the best of the day.
Schauffele and Cantlay have been close friends since being paired together at the 2019 Presidents Cup in Australia, and they combined to win the Zurich Classic this season.
"If only it was a combined score again this week, we would be doing well," Cantlay said jokingly. "It's always nice to be out with him, if he's on my team or if he's not. I'm going to go out there tomorrow and try as hard as I can and let the chips fall where they may."
Schauffele is looking for his sixth individual title and first since the 2019 Sentry Tournament of Champions. He also is shooting for his sixth straight top-20 finish. He and Cantlay finished tied for 14th last week in the U.S. Open.
"I've been looking forward to playing with Pat in a final round," Schauffele said. "We don't get paired together very often in regular tournaments, only in those team ones. So there's a certain level of comfort we have playing with each other, and hopefully that pays off and hopefully we can make a lot of birdies."
Theegala had an eagle on 13 to go with four birdies. The 24-year-old Californian hit his second shot on the par-4 17th over the course's signature lake to about a foot from the pin, briefly tying Schauffele for the lead. But he bogeyed the final hole.
He is looking to become the 18th player to get his first tour win in Connecticut. Ken Duke was the last to do it in 2013.
"I'm definitely going to be nervous, definitely going to be excited," Theegala said. "Every single week I'm out here, I feel like I'm getting more and more comfortable."
Former U.S. Junior champion Michael Thorbjornsen shot a 66 to put himself in contention. He started the weekend at 7 under, just the third amateur to make a PGA Tour cut in 2022. The Stanford star is in a group of four tied for seventh place, but he said he wasn't feeling much pressure.
"One thing that might help is winning or coming in second or third, I'm not getting paid either way, so it's another tournament for me," he said. "It's just another round for me, and I'll just try to go out there and do the same thing I did today."
Top-ranked Scottie Scheffler was also in that group after shooting a 65. He began the weekend 9 strokes behind Schauffele.
"Maybe I'll go out tomorrow and do something crazy and we'll see what happens," Scheffler said.
First-round co-leader Rory McIlroy (72) got in trouble early Saturday, hitting his tee shot on No. 2 off a nearby tree and into the tall grass 108 yards across the fairway to the right. After a 39 on the back nine Friday, he shot 36 on the front nine Saturday and finished 2 over for the day and 6 under for the tournament, 11 strokes off the pace.
There was also a buzz at the tournament Saturday around a player who was no longer even in Cromwell.
Jason Kokrak was disqualified Friday after launching his final shot on the ninth hole over the green and the fence behind it. Kokrak, who would have missed the cut anyhow, left the course without replaying the shot.
William McGirt, who was playing in the same group, said Kokrak simply didn't see any point in finishing the hole.
"He was like, 'I'm not going to hold anybody up,'" McGirt said. "He didn't storm off the golf course."