He had to settle for a 71.
The final group of Spieth and Schauffele started well, both making four pars each to begin with.
Kevin Chappell made two double bogeys, the last one on No. 17 that derailed his hopes. A double-bogey 6 after finding a bunker off the tee at the second hole was followed by a bogey at the next as Kisner struggled to deal with an early stiff wind.
Watch Tiger's wedge shot below. They ran out of holes. But the closing holes are treacherous, and despite flinching on a tee shot at the 18th because of a spectator bellowing during his backswing, he managed to give himself a 5-footer for birdie that he missed.
Molinari raised his fist and shook it lightly before slamming it for emphasis.
Then, he waited in the trailer to see if anyone could catch him. At one point, he went over to the practice green, but not to prepare for a playoff.
'I saw it on maybe No 7 or 8 green - and it was an accident, ' he said.
But while past year Spieth survived a wobble in the final round at Royal Birkdale to take the title, this time he was too erratic, not recovering from a bogey at the fifth that was followed by a double-bogey at the long sixth where his second shot found a gorse bush.
Jurgen Klopp gives details on Joel Matip injury
Clear cut chances were few and far between in the opening 15 minutes, despite both sides playing at a good tempo early on. Obviously we can not say more about this now, but that's of course the most negative thing about the day.
Toronto shooting: Victims ‘spread across many blocks’
Victims are being sent to local hospitals. "Trauma Centre's will only be taking the most serious". Breaking News Toronto said: "Two more victims located with Gunshot wounds to the lower legs".
Open result will sting for a little bit, says Tiger Woods
Woods played his "one bad swing" at the 18th, but lady luck intervened to keep his ball out of Barry Burn and in thick rough that at least gave him a shot.
"Just disbelief, to be honest", the 35-year-old said.
"The course bit me a few times the first couple of days, but then to go bogey-free over the weekend on a course like this is incredible". Three other players are within three shots, while Tiger Woods is in a group of eight golfers at 5 under. "He showed really good sportsmanship with me".
"It didn't feel any different to be next to the lead and knowing what I need to do, " he said.
Woods was four shots behind. It felt like old times at the British Open, as familiar as his Sunday red shirt and the swarm of fans that cheered his every shot. Woods dropped his putter in disbelief when a birdie attempt refused to drop on 13, but he made birdie at the par-five 14th to put his name at the top of the leaderboard - a development that had seasoned golf hacks snapping photos of the huge media scoreboard. While Woods was getting off to a hot start, his fellow competitors were going the opposite direction.
Schauffele had to hole out a wedge on the final hole and checked up well short of the hole. Still in range, he couldn't get close enough for a birdie when it mattered.
McIlroy, who grew up watching Woods, said the 14-time major champion is not feared like he was during his prime. She just had a baby and lost the Wimbledon finals. He has won The Open Championship, still known colloquially to many as the British Open, three times, including back to back triumphs in 2005 and 2006.
"Serena will probably call me and talk to me about it because you've got to put things in perspective", said Woods who eventually finished tied for sixth, three shots behind playing partner and champion Francesco Molinari. I know he is going to work on it and make it better, but he still has the PGA Championship.