The former record vanished under a cloudy sky at 7:16 p.m. when Cantlay made a 2-foot putt at No. 18.
"I just felt like I could roll anything in, and I wasn't worried about my stroke whatsoever," said Cantlay, who needed just 24 putts, 10 of which were one-putts.
His 60 tied Tommy Bolt's tournament record set at Wethersfield Country Club in the 1954 Insurance City Open.
Cantlay, the winner of the Jack Nicklaus Award as college player of the year (UCLA) and the Phil Mickleson Award as freshman of the year, followed his opening round 67 Friday with his record 60. His 13-under 127 was four shots better than Webb Simpson (66-65), Vaughn Taylor (65-66), D.J. Trahan (69-62) and Alexandre Rocha (65-66).
Andres Romero also is 9 under after carding a 64 and being 3 under over the first five holes of his second round.
The second round was suspended because of darkness at 8:01 p.m. Seventy-seven players will complete the second round starting at 7 a.m. Saturday. The third round will consist of threesomes off both tees and will start at about 11 a.m.
The revised schedules were necessary after the first round was suspended because of a lightning threat before noon Thursday and never resumed because of heavy rain. The first round ended at 2:12 p.m. Friday. Jim Renner held the lead at 63, but he shot 74 in the second round.
It was one wild - and, thankfully, not wet - day at the Travelers before an estimated crowd of 50,000.
There were players finishing up their first rounds, while others were in their second rounds. Chris Couch hit three shots to complete his 18th hole of the first round. Then he played nine holes of his second round before darkness ended his day at 7 under overall.
Others, like Cantlay, played 36 holes.
"It's just astonishing to be that young and playing that well, especially in these kinds of conditions with these kinds of players out here" said Billy Horschel, who played in Cantlay's group with Sunghoon Kang. "He has got a level head on his shoulders and doesn't let things get to him."
Cantlay hit 10 of 14 fairways and 15 of 18 greens in his 60. His accuracy and impressive focus on the course came after he had tied for 21st place as the low amateur in the U.S. Open Sunday. He said it bolstered his confidence before making his first appearance in a PGA Tour-sponsored tournament.
He started his second round with a 12-foot birdie putt from the fringe on the first hole. A hybrid at the par-5 fifth preceded a 12-foot birdie. Then he recorded birdies at No. 6 (8 feet), 8 (30) and 9 (4).
Another sweet hybrid at the par-5 13th allowed him to make a 19-foot eagle putt, his second eagle on that hole. Then came a gap wedge to 8 feet for another birdie at 14.
"There was a different set of butterflies," Cantlay said of his U.S. Open appearance. "But other than that, I felt real comfortable the last five rounds I've played. So it hasn't been any different than a college tournament or any other tournament, for that matter."
His father Steve, who was in attendance, had a different view.
"This was the most memorable round he has ever played, considering everything," Steve said.
His son had shot a 60 before, though, at Virginia Country Club in Long Beach, Calif.
It didn't compare to Friday's performance in the second round.
After parring 15 and 16, Cantlay made a 6-foot birdie putt at the par-4 17th to move to 9 under on his round.
"I knew where I was, and I knew I needed to make eagle  on 18 for 59," Cantlay said.
He almost holed his 8-iron second shot from 152 yards. It landed 5 feet beyond the cup and spun back and stopped 2 feet, 4 inches from the cup.
He took one practice stroke and knocked the putt into the center of the hole. He gave a slight wave to the few fans who remained to see history.
"He really never shows that much emotion at all," caddie Chris Roth said. "He was pretty content the entire day. He doesn't ever get angry. He just tries to stay calm."
As he walked up a steep hill to get to the scorer's trailer, he tossed his Titleist 1 ball into the cheering crowd. Ellen Hesketh, 11, gleefully caught it.
"We came down from Granby and started watching him at 15," said Ellen's father, Scott. "I said he's going to get hot, let's stay with him."
After Cantlay did all of his interviews, he autographed his record-setting golf ball.
Ellen, clutching the ball with both hands, said, "It's going in a special case. This was history."