Norway's Kristoff outsprinted Danish world champion Mads Pedersen after 156 km around Nice.
Vingegaard laid the foundations of his victory in the 10th stage
The overall standings remained unchanged at the top with Thomas leading defending champion Froome by one minute 39 seconds and Dutchman Tom Dumoulin by 1:50.
'It's a big emotion because I've won on the Tour. I haven't won (a race) since the start of the season. It's great to make it. It was tough but I'm super happy to have won.'
Spain's Gorka Izagirre took second place and Yates finished third, 15 seconds behind.
World champion Peter Sagan claimed his third 2016 Tour de France stage victory when he pipped Alexander Kristoff on the line at the end of the 16th stage, a 209-km ride from Moirans-en-Montagne on Monday.
Andre Greipel confirmed he was the sprint king at this year's Tour de France when the German outpowered his rivals to win the 15th stage on Sunday.
Mark Cavendish claimed his 30th Tour de France victory and fourth in this year's race when he left sprint rival Marcel Kittel trailing at the end of the 14th stage on Saturday.
Geraint Thomas tightened Team Sky's grip on the Tour de France when he handed the British outfit their sixth title in seven years on Sunday and there is no sign that their domination will end anytime soon.
Briton Chris Froome won his second Tour de France title in three years on Sunday to enhance his growing reputation as a grand tour specialist.
Slovakian Peter Sagan elbowed Mark Cavendish off balance as the Briton was trying to force his way between him and the safety barrier, and Cavendish was sent crashing heavily.
Briton Chris Froome cemented his status as one of the greatest Tour de France riders when he secured his third title on Sunday after a three-week rocky ride.
Alberto Contador will cement his status as the best grand tour rider of the modern era if he emerges as the winner of the Big Four's battle royale at the Tour de France -- the most highly anticipated race in decades.
Check out the main contenders for this year's Tour de France, which starts on Saturday in Utrecht, Netherlands.