Topsy-turvy day at Open

Dustin Johnson at least gets one more round to try to redeem himself in the US Open.

So does the USGA.

The best players in the world were no match for a Shinnecock Hills course that even the USGA conceded got out of hand yesterday. Putts were rolling some 50 feet by the hole and over the green.

No one from the final 22 groups could match par. Phil Mickelson intentionally broke a rule on the 13th when he trotted to his ball rolling by the cup and swatted it with his putter as the ball was still moving.

‘‘It was a very tough test, but probably too tough this afternoon,’’ said Mike Davis, the USGA’S chief executive. ‘‘We must slow the courses down, and we will.’’

It was too late for one of the wildest shake-ups at the US Open.

Daniel Berger and Tony Finau, who started the third round 11 shots out of the lead, each shot 4-under 66 before Johnson hit his first shot. Johnson faced greens that made him feel as though he were putting on glass, and it was like that to the very end.

Johnson, who started with a four-shot lead, barely nudged his 17-foot birdie attempt on the 18th hole and watched it roll — and roll — 8 feet by the cup. He missed the par putt coming back and signed for a 77 to fall into a fourway tie for the lead.

‘‘I didn’t feel like I played badly at all,’’ Johnson said. ‘‘Seven over usually is a terrible score, but with the greens the way they got this afternoon, I mean they were very, very difficult. ’’

At least he still has a chance, and he had plenty more company at the top than at the start of the day.

Johnson joined Berger, Finau and defending champion Brooks Koepka (72) at 3-over 213, the highest 54-hole score to lead the US Open since the fabled ‘‘Massacre at Winged Foot’’ in 1974.

It was the first time since Oakmont in 2007 that no one was under par going into the final day. With wind that was stronger than expected, and a few pin positions that turned the US Open into carnival golf, it was easy to see why.

Mickelson brought plenty of attention to the 13th hole, where anything that ran by the cup was headed off the green. Worst yet might have been No 15, where Piercy had a 30-foot birdie putt that finished rolling 75 feet away off the green. Koepka hit an approach to near the hole, and it moved a few inches to the right, and then a few more feet, and soon it was in a bunker.

‘‘You were seeing shots that were well played and rewarded,’’ Davis said.

Berger and Finau, who made the cut with one shot to spare, will play in the final group.

‘‘I barely made the cut. Going into today, I needed something special to happen to even have an outside chance,’’ Finau said as Johnson and Scott Piercy were making their way down the first fairway in the final group. ‘‘Whether I do or not at the end of today, I’m really happy with where I’m at.’’

Right behind them will be the last two US Open champions. Koepka made only two birdies in his hard-earned round of 72, leaving him poised to become the first player since Curtis Strange in 1989 to win back-to-back in the US Open.

Only three players broke par, not all before the final groups teed off.

‘‘If they’d have shot 4 under this afternoon, it would probably have been the best round of golf anybody’s ever seen,’’ Koepka said.

Two other major champions – Justin Rose and Henrik Stenson – were right behind, and both had a share of the lead at one point. Both had three straight bogeys. Rose wound up with a 73 and was one shot behind at 214. Stenson had a 74 and was another shot back.

The return to Shinnecock Hills was supposed to make the US Open feel like a traditional test that felt more like survival.

‘‘Be care what you wish for,’’ Rose said. ‘‘We’ve all been asking for a real US Open again. So I guess we got one for sure this week.’’