It was on the eighth hole where Clark’s advantage could have fully unraveled, when his second shot landed in green-vicinity foliage that looked more receptive to a scythe than a club. Clark’s first escape attempt went all of eight inches, according to tournament officials — a sum that seemed about eight inches too high. He escaped by lifting a shot over the green into the right rough and ultimately saved bogey, his lead shaved to a stroke.

Clark and McIlroy both played the front nine to 34, one under. For both, though, the back nine had typically been more bruising. Their positions on the leaderboard were static until the 14th hole, when McIlroy’s wedge shot sent his ball thumping into the side of a bunker. Granted free relief, he dropped into the fescue near the hole but could do no better than departing the green with a bogey.

Clark’s experience was far more comfortable, his second shot leaving him less than two dozen feet from the par-5 hole’s pin, setting up an eagle opportunity. Clark’s putt went just to the right of the cup, but a subsequent birdie attempt dropped, building his margin to three strokes.

It was brief. Clark missed a par chance on the 15th hole when his putt did not sufficiently break, and then his tee shot on No. 16 wound up in a bunker. Despite dazzling wedge play with his third shot, a short putt soon enough lipped out for Clark’s second consecutive bogey.

Down by a stroke, McIlroy, who struggled on the greens for much of the day, barely missed a birdie putt on the 17th hole, his familiar anguish reappearing and the prospect of the Open’s first playoff since 2008 dwindling a bit more.

Finishing at nine under, McIlroy recorded a par on the final hole, where Clark had made par or birdie during each of the first three rounds. If Clark could stick to that history, the galleries knew, he would be a major champion — just as he concluded last month he was all but ready to be.

Par, to stay at 10 under, to finish at 10 under. His eyes glistened.

He had played big.