Quintana, 22, was the only rider capable of clearing away from the main pack, dominated by Wiggins' Sky team, on the ascent of the Dauphine's main mountain challenge, the Col de Joux Plane.
After plunging down the twisting drop to Morzine, Quintana finished 16 seconds ahead of Australia's Cadel Evans, with Spain's Dani Moreno third and Wiggins fourth, 24 seconds back.
"I didn't feel too great in the first part of this stage, but I managed to recover well enough to go all out in the second part," Quintana, whose only previous significant success was the mountains prize on the 2011 Tour of Catalonia, said.
"I only had a few seconds advantage at the top of the climb, it was touch and go."
After his compatriots Rigoberto Uran and Sergio Henao took top 10 places in the Giro d'Italia, Quintana expressed his pride at being a part of a new wave of Columbian cyclists that also included Cayetano Sarmiento, now the Dauphiné's King of the Mountains.
"With him in the podium, too, and me as well, it's an important triumph for both of us. Cayetano is like a brother to me," Quintana added.
Wiggins' Sky team kept up a ferocious pace on the Joux Plane's 10 percent slopes, with Italian favourite Vincenzo Nibali and German time trialist Tony Martin, previously second overall, among those to fall behind.
Evans made a timid move over the top of the Joux Plane as part of an eight-strong pack containing three Sky riders, including Wiggins, and a determined attack on the drop down to Morzine, but could only gain eight seconds.
Wiggins remained the overall leader with one day remaining, while his Australian team-mate Michael Rogers confirmed Sky's dominance by moving up to second one minute and 20 seconds behind, with Evans in third at 1.36, and another Sky rider, Chris Froome of Great Britain, in fourth.
"Have you seen how strong we were today?" Wiggins said.
"They made my job a lot easier, although it was tough all the same.
"Cadel attacked, he got a bit of an advantage, but I didn't want to take any risks."
While Wiggins and Sky's performance on Saturday will make them among the favourites for the upcoming Tour de France, the remaining hurdle to a second Dauphine title is Sunday's short but mountainous leg from Morzine to Chatel.
"The Dauphine isn't over yet, but we've done the hardest part now. We should be ok but you never know. It's too early to say that I've won,"
Another Tour de France favourite, 2010 winner Andy Schleck of Luxembourg, withdrew from the race after failing to recover from his injuries in Thursday's time trial.
Stage six results:
1. Nairo Quintana (Colombia / Movistar) 4:46:12"
2. Cadel Evans (Australia / BMC Racing) +16"
3. Daniel Moreno (Spain / Katusha) +24"
4. Bradley Wiggins (Britain / Team Sky)
5. Pieter Weening (Netherlands / Orica)
6. Chris Froome (Britain / Team Sky)
7. Vasil Kiryienka (Belarus / Movistar)
8. Jurgen Van den Broeck (Belgium / Lotto)
9. Michael Rogers (Australia / Team Sky)
10. Haimar Zubeldia (Spain / RadioShack)
11. Richie Porte (Australia / Team Sky) +34"
12. Janez Brajkovic (Slovenia / Astana) +44"
13. Tejay Van Garderen (U.S. / BMC Racing) +1:12"
14. Tiago Machado (Portugal / RadioShack) +1:30"
15. Alexandre Geniez (France / Argos) +2:05"
16. Wilco Kelderman (Netherlands / Rabobank)
17. Pierre Rolland (France / Europcar) +2:08"
18. Guillaume Levarlet (France / Saur - Sojasun)
19. Jerome Coppel (France / Saur - Sojasun)
20. Bruno Pires (Portugal / Saxo Bank) +2:15"