Steve Cummings (MTN-Qhubeka) won the 178.5km stage from Rodez, coming from behind a small gap to Thibaut Pinot (FDJ) and Romain Bardet (AG2R La Mondiale) to claim the victory into the final sprint.
Further back, the other defining moment of the stage happened when Quintana (Movistar) chose to power ahead halfway through the steep slopes of the final ascent, a three kilometre test with an average gradient of 10.1 per cent.
While yellow jersey wearer, Chris Froome (Sky) reacted quickly to successive moves from Qunitana, the Colombian's efforts quickly dropped Tejay van Garderen (BMC), who finished 39 seconds behind Quintana. The time difference was enough to see Quintana jump to second in the overall classification, with van Garderen dropping back to third.
"I'm really happy with having climbed onto second,” said Quintana. “We knew that patience would bring this place to us, but our real goal, the one we're focused on, is taking place number one.
"We didn't have this stage and climb marked down for an attack, but I felt strong today and we thought that, after the fast pace in the last few days, wear and tear would be more evident.”
Spectators on the side of the road provided Quintana with extra motivation keep putting power through the pedals.
“I was really amazed to see so many Colombians again today at the finish; they must be really excited about this, as much as I am to see them, and this brings passion and huge support to me in order to keep pushing,” he said.
At the end of the stage, Froome outsprinted Quintana by one second on the line. The Briton holds an advantage of 3min 10sec over the Colombian as the Tour approaches the next great test of climbing in the Alps.
“We have worked hard with the team through all these days,” said Quintana. “We found a chance to gain time today and we're staying confident and determined to try some attacks when the big mountains are back, maybe still being able to go after that yellow dream.”
While Quintana worked to distance his competition, Movistar’s Alejandro Valverde went on to find his own rhythm, while being careful not to help any of his rivals eat into the lead Quintana was establishing further ahead.
"Taking them into Nairo's wheel would have been really bad. So I waited, then kept my own pace not to lose much time.” - Alejandro Valverde
When the timing was right, Valverde chased down Alberto Contador (Tinkoff-Saxo), attacked and finished the stage only three short seconds behind his Colombian team-mate.
“When I reached him, Contador asked me for some turns and I told him I couldn't take them, because Nairo was ahead. This is racing: he's doing his job, mine is to take care of Nairo, and he was the one who had to push,” said Valverde who retained fourth in the general classification.
Valverde now sits 4min 2sec behind Froome in the overall standings and is just 30 seconds away from van Garderen.
Despite losing valuable time to his rivals, van Garderen was matter-of-fact about his abilities on the decisive climb, which summited 1.5km before the finish.
"I just tried to stay within myself and limit the time loss," said van Garderen. "It is a pity to move down a place on GC, but the podium is still very much a realistic goal.
“It was a difficult climb. On those gradients, that is where I tend to struggle the most. The Alps are better suited to my characteristics. I am still looking forward and I am still feeling good.”
While he lost time to Froome and his Movistar rivals, van Garderen was optimistic about time gained over Geraint Thomas (Sky) and Robert Gesink (LottoNL-Jumbo) who also slipped down the leaderboard on last night’s stage.
Two stages remain before the second rest day.
Stage 15 connects Mende with Valence across 183km, with two small ascents in the opening part and the Category 2 climb, L'Escrinet just under 60km before the finish.