Francesco Molinari is the first Italian major champion. (Peter Morrison/Associated Press)

The cheers as he walked up the 18th fairway were exuberant, but this time they weren’t just for 42-year-old Tiger Woods.

Woods, who had battled and for a time occupied the top spot on the British Open leader board Sunday, was overshadowed by his playing partner. Italy’s Francesco Molinari put together a solid final round Sunday, winning the Claret Jug with a birdie on the 18th hole. That put him at 8-under, two strokes ahead of Xander Schauffele and a number of other golfers. Woods, trying to win his 15th major, finished at 5-under.

As the day progressed, a number of golfers and Molinari were in contention, but Woods couldn’t narrow the gap. Woods trailed the co-leaders, Molinari and Schauffele, by two strokes as he headed to the 18th hole and he sent his shot down the left side of the fairway, asking himself, “What are you doing?” He saved par, but Molinari’s birdie was the killer.

A five-time European Tour champion, the 35-year-old Molinari won his first PGA Tour event earlier this month, the Quicken Loans National in Potomac. His victory Sunday, his first major win, made him the first Italian to win the British Open since it began in 1860.

As he left the course, Woods hugged his kids, 11-year-old Sam and 9-year-old Charlie, a reminder that he had been hoping they’d see their father win a major. A victory would be extra meaningful, he pointed out Saturday, because his kids were too young to have seen him at his best. Daughter Sam was a baby the last time he won a major and son Charlie had not yet arrived.

It was that kind of day. (Harry How / Getty Images)

“I want them to see Dad do what he’s done for most of his life,” he told NBC, “and make them feel and watch what their father can do.”

They saw some vintage Tiger, but there wasn’t enough of it. In a sign of the struggles that were to come, Woods, with a one-stroke lead, sent a shot on 11 wide into the tall grass. His next shot elicited an “Oh, God,” as it sailed past the fairway and luckily struck the phone of a spectator, who was none the worse for having helped Woods avert utter disaster. As it was, Woods was left with a lengthy shot from thick grass. Hitting under the ball, it went just a few feet. His putt missed by an inch, leaving him with a putt for bogey. He missed and the double-bogey dropped him to 5-under. A bogey at 12 dropped him to 4-under, two strokes off the lead.

He reclaimed that lost stroke with a birdie on 14, the easiest hole on the course, and was at 5-under, two strokes off the lead.

As he fell, the leader board was jumping, with a number of players taking turns atop it. Molinari, held the lead (with Schauffele) after a birdie on 14 put him at 7-under. Justin Rose quietly ascended the board and was in the clubhouse at 6-under along with Rory McIlroy while Jordan Spieth, Kevin Chappell and Schauffele joined in the battle for the Claret Jug.

After a strong start, Woods found himself taking up residence in bunkers and with poor lies. At first, he was coping with disaster well. Although he found a bunker on nine, Woods managed to send his shot within four feet of the hole — and he promptly sank the putt. He was in a good place at the turn and so was his partner for the day, Molinari. He’s one shot back at 6-under and Molinari and Woods are the only ones bogey-free to that pointy.

Woods, showing that he still excites crowds, just missed a 25-foot putt for a share of the lead on the seventh hole. Instead, he remained at 7-under, one shot off the lead. Although he found the bunker on No. 8, he converted for par after a sweet shot to within four feet of the hole.

Woods opened his day at five-under par, four shots back of the leaders, fellow Americans Kevin Kisner, Spieth and Schauffele. Woods made his first move at four, sinking a 15-foot birdie putt that nudged him up the leader board, three strokes off the lead. With his game steady and on point, the leaders found themselves struggling.

Woods looked ready to make a huge move on the sixth hole and instead settled for a merely big, big move. After his tee shot just missed a bunker, his long bid for an eagle just missed and left him with a short birdie putt. He confidently put the ball in the hole and moved to two strokes off the lead at 7-under par.

Meanwhile, Spieth and Schauffele each dropped a shot at No. 5, falling to eight-under, and Spieth encountered real trouble on No. 6 with his ball in the routh. Kisner had an earlier stumble with a double-bogey at No. 2.

Woods appeared to be in position to take another stroke off his score on No. 5, but his approach shot rolled away from the hole, leaving him with about a 30-foot putt. He got within about a foot and ended up with par on the hole. If that’s the only bad luck he has today . . . he’ll take it.

If there was any doubt about Woods’s ability to excite crowds, it ended on the first hole. Woods’s tee shot found the fairway, with his approach shot landing about 15 feet from the pin and bringing a roar from the crowd. His putt was perfect, lacking only a little speed. It slid to the left for par, a sufficient way to begin the final round on a day when the winds are kicking up and sending sand into golfers’ eyes.

Woods got to be in contention on a Sunday by firing a 5-under 66 on Saturday, a score that was his best weekend round at a major since 2010. There were moments Saturday when he even held a share of the lead. He has not done so after a round at a major since the second round of the 2012 PGA Championship.

Paired with Molinari, Woods arrived Sunday morning at Carnoustie in his signature Sunday red and black, ready to tee off at 9:25 a.m. Eastern with the winds on the coast of Scotland gaining speed.

“I’ve had a chance to win. Given what happened the last two years, I didn’t know if that would ever happen again,” Woods said Saturday. “But here I am with a chance Sunday in a major championship.”

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