Adding to the pressure was knowing that Royal Birkdale, with a clear sky until the final hour and barely any wind, was never more vulnerable. No one took advantage quite like Branden Grace, who finished birdie-birdie-par and became the first player to shoot 62 in a major.
More than half the field broke par. Spieth was among seven players who shot 65 or better.
"You knew scores would be lower," he said. "It's tough to hold a lead when par is not necessarily a great score, when you want to watch out and play a little safer."
He was at 11-under 199, stealing a birdie at the end when his approach into the 18th stayed just left of the bunker and left him 20 feet away. Spieth clenched his fist when it dropped for birdie, and then Kuchar missed from about 12 feet.
They will see each other again tomorrow, and they put some distance from everyone else.
Austin Connelly, who grew up in Dallas and shares a swing coach with Spieth, extended his remarkable run with birdies on his last two holes for a 66. The 20-year-old who plays under the Canadian flag was six shots behind at 5-under 205, tied with U.S. Open champion Brooks Koepka, who had a 68.
Grace wound up seven shots behind even after his 62.
Missing from the mix was Rory McIlroy, who looked to be a big threat when he began with three birdies in five holes, driving the green on the shortened par-4 fifth hole. He lost it around the turn, making back-to-back bogeys, and then a double bogey at No. 10 when he blasted out of one pot bunker left of the fairway and it spun toward another, resting in the thick collar.
McIlroy had a 69, rarely a bad score in the third round of a major. This one left him nine shots behind.
"If you keep it in play, it's almost hard to make a bogey out there, you know?" McIlroy said. "I've always been good when I get off to fast starts, being able to keep it going, and I didn't today. And I needed to - that's the disappointing thing."
Ian Poulter felt even worse. Still lurking, he ran off three straight bogeys early on the back nine and shot 71 to fall nine back.
Spieth was rarely in trouble. He stuck to his simple plan and kept making all the right putts. He never lost the lead after any hole, though Kuchar kept close. He matched Kuchar's birdie on the third hole to stay one shot ahead.
An even bigger moment came at the 15th, when Spieth ran his 60-foot eagle attempt 10 feet by the hole. Kuchar lagged his eagle putt to tap-in range to reach 9 under and momentarily join Spieth in the lead, but only until Spieth poured in the tricky birdie putt.
Kuchar's big lapses came on the 16th when he drove into a pot bunker, could only blast out to the fairway with a sand wedge, hit an indifferent shot to the green and then three-putted for double bogey. Just like that, he was three shots behind.
Kuchar got up-and-down from a pot bunker on the par-5 17th when Spieth made par, but as usual, Spieth had one last birdie in his bag.
"I played well today," Kuchar said. "Certainly, I'm not out of it. I'm playing some good golf. I'm very excited for tomorrow."
It will be the first time the 39-year-old Kuchar plays in the final group at a major. Spieth, who turns 24 next Thursday, has been there before. It will be his third time playing in the final group at a major. He won the Masters with a four-shot lead in 2015 and lost the Masters the following year with a one-shot lead at the start of the final round, and a five-shot lead at the turn.
Spieth has a chance to join Jack Nicklaus as the only players to capture three different majors at age 23. He won the Masters and U.S. Open two years ago, and then finished one shot out of a playoff at St. Andrews.
Nicklaus won the U.S. Open at 22, and then added the Masters and PGA Championship the following year.
The forecast was for stronger wind on Sunday, which should be a stronger test for Spieth going for his third major, and Kuchar going for his first.
