Poland's Adrian Meronk sank the decisive putt as Continental Europe held off Great Britain and Ireland in Sunday's singles to win the inaugural Hero Cup in Abu Dhabi.
Smith used a run of five consecutive birdies to card an 8-under-par 64, overtake Northern Ireland's Rory McIlroy and win The Open by one stroke for his first major title at St. Andrews in Scotland.
Fitzpatrick's one-stroke lead at the 18th tee "is going to be shown probably for the rest of US Open history", said rival Will Zalatoris.
Woods, in his second start after a car crash 15 months ago nearly cost him his right leg, appeared dejected and in pain as he trudged off the 18th green at Southern Hill Country Club.
Rory McIlroy delivered his best opening round in a major since a 65 at the 2011 US Open which he had won for his first major title.
The 26-year-old South Korean recovered from a bogey on No. 17 with a birdie on the final hole to finish at 11-under 277 and win for the fifth time on the LPGA Tour.
Superstar golfer Tiger Woods is testing his ability to play this week's 86th Masters following a serious right leg injury last year.
The former world number one, who has not played since suffering career-threatening leg injuries in a car crash 10 months ago, will play in the December 16-19 tournament alongside his son Charlie.
The Ryder Cup was postponed last year because of the Covid-19 pandemic.
US Open champion Jon Rahm added further accolades to a stellar campaign on Tuesday as he was named the PGA of America Player of the Year and also collected the Vardon Trophy.
Suat Ari is a physical education teacher in a Turkish village who has inspired scores of students to compete in national games, and was selected as a Changemaker by the Sabanci Foundation this year.
Korda finished 19 under, three strokes ahead of Lizette Salas, after a 4-under 68 in her final round.
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