In doing so, the Colombian secured the King of the Mountains jersey and that of the best young rider.
As if that was not enough, Quintana supplanted Alberto Contador to claim second place overall ahead of Joaquim Rodriguez, with Contador relegated to fourth.
"I'm crying tears of joy," said the 23-year-old, who has made an amazing journey to find himself one of the toasts of the Tour.
"I never imagined I could be in this position."
Quintana has one of the more remarkable stories in the peloton, raised in stark poverty outside of Combita, Colombia. His parents had to save up to buy him a battered second-hand mountain bike not for fun, but to try and spare him some of the dangers presented by his nine-mile journey to school each day.
Instead it has propelled him to the top of his sport at warp speed.
"What happened today [Saturday] took a huge amount of work," he said through an interpreter. "I have the physical condition that God gave me and that my parents gave me, but I also did what I did today thanks to my team.
"One year ago I didn't even imagine being able to ride in the Tour de France, I only became a professional one year ago, ever since I was a little boy I never even imagined dreaming of this."
Although he featured as an outside bet among the contenders coming into this Tour due to his obvious ability as a climber, Quintana arrived in Corsica three weeks ago as a support rider for Movistar team-mate Alejandro Valverde.
But when the Spaniard's Tour challenge was blown off course on the windy road to Saint-Amand-Montrond on stage 13, Quintana stepped up.
He said: "When my sporting director said to me I would be taking the lead of the team I said yes, obviously.
"But I also said to him that if one day my legs fail me because the Tour is such a fast race, I might have to apologise.
"He said, 'No, you do your best', and today we saw that I could do well.
"Now I'm full of hope. This really encourages me to work even more and maybe in 2015 we will try to win the Tour de France."