The 21-year-old from China became the fourth player to shoot 63 in the final round of the British Open - after Jodie Mudd (Royal Birkdale, 1991), Payne Stewart (Royal St. George's, 1993) and Henrik Stenson (Royal Troon, 2016) - and the 30th player overall with 63 in any major round.
Birdies at 8, 9 and 12 around the turn were followed by four more in the final four holes to leave him on six-under and the first Chinese player to place in the top five in a major.
The score was the all-time low in a major until Saturday, when South Africa's Branden Grace broke new ground with an unprecedented 62 in the third round. "It's kind of a dream come true, you know". "You see some guys get a little bit scared, but he kept going so it was really special to see".
"That's not the same number as Grace, but that's as good a round", Els said.
"Glad to see I holed everything". Now I'm feeling awesome, it is unbelievable actually. "So quite happy out there". When I hit a bad shot I just told myself to hang in there and try to hole the putt.
Li, whose game his fine tuned by his coach Jamie Gough, the brother of former Scotland footballer Richard, made his breakthrough on the European Tour in 2015 when he won the Shenzhen International in his own backyard before claiming another victory in his native land last season with a win at the Volvo China Open.
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Four-time Major victor Ernie Els, 47, was impressed with Li's performance.
When Li won the Nanshan China Masters at the age of 19 in 2014, he became the youngest ever victor on the OneAsia Tour.
In 1971, Taiwan's Lu Liang-Huan, sporting a pork pie hat wherever he went, finished second to Lee Trevino of the United States, missing out on the Claret Jug by a single stroke.
Li is just the third Chinese to qualify for a major golfing competition and it completes an impressive year for the starlet. "Huge", Li said, according to a report on THE OPEN website. Li's mood did not improve at the French Open when he tossed his broken putter into a lake during the first round and his mother had to wade into the water to retrieve it.
Li had gone 69-73-69 through his first three rounds, solid if unspectacular form. "I have played in the U.S. Open once, now The Open, and I look forward to one day playing in the PGA Championship and the Masters too".