"I would have liked to win the stage, but the most important thing for me was to keep the yellow jersey and that was the case," said Vingegaard.
"I knew that I had no chance in the sprint against Pogacar. I tried a surprise attack, it didn't really work!"
Adam Yates is in third place and his twin brother Simon is fourth, while Spain's Carlos Rodriguez rounds out the top five.
Pogacar raised his arms and celebrated at the line despite not having been able to shake off Vingegaard, which he repeatedly tried to do on the last hill.
"I finally felt myself again today after a bad week," said the 2020 and 2021 champion.
"I felt good from start to finish, after several very difficult days on the bike."
There were six mountains to negotiate on Saturday with the last two being category one climbs.
Pogacar had promised an explosive finale, but he was tracked every kilometre of the way by his Danish rival.
Vingegaard and Pogacar have thrilled fans with their struggle for supremacy on the 21-day race which started in Bilbao in the rolling hills of the Basque Country.
The Dane crushed Pogacar in the key stage 16 time-trial on Tuesday, putting 1min 38sec into him on the 22.4km run.
The following day, on the hardest mountain stage, Pogacar cracked, shouting into his team radio "I'm dead, I'm gone."
And so it proved to be as he lost almost seven more minutes on the steep and punishingly long climb to Courchevel.
Runner-up to Pogacar in 2021, the softly-spoken Vingegaard was the only rider to challenge the Slovenian prodigy in the high mountains.
In 2022, Team Jumbo-Visma's Vingegaard went one step higher and won the title at altitude, and it proved to be the case again in 2023.
Saving face
Adam Yates won the opening stage back in Bilbao, and was on flying form at this Tour, ending on the podium alongside Pogacar, who won two stages.
That is a decent return given Pogacar broke a wrist in April and Yates has just joined Team UAE.
"We didn't win but we got another stage and two places on the podium," said Yates after riding into the press room on his black Colnago bike.
"When you have a leader like Tadej it's so enjoyable."
Huge crowds turned out to greet local hero Thibaut Pinot who was cheered up every mountain as he finished seventh on the day.
"I did what I could," said a crying Pinot who was given a rousing reception atop the Vosges mountain as he competed in his final Tour.
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