The Movistar rider finished ahead of Ryder Hesjedal (Garmin-Sharp) and Pierre Rolland (Europcar) at the end of the weather affected 139km stage which passed over the legendary Gavia and Stelvio climbs before finishing atop the Val Martello.
"I did the last climb at my own rhythm but I gave it everything I had," said the 24-year-old Colombian.
"Since the start of the season, I think I've shown my runner-up place at the Tour de France (in 2013) was no fluke.
"In this Giro I've encountered a few problems but I've never lost hope. The team have been right behind me and kept my confidence intact."
Quintana's hopes of competing for the overall title appeared to suffer a blow when injury and illness saw him fall 3min 29sec behind Uran (Omega Pharma-QuickStep) after the first two weeks of racing.
But on the first of several gruelling days in the mountains in this final week, he rode himself into the race lead as Uran and, notably Australian Cadel Evans (BMC), ultimately failed to follow Quintana's wheel on a rain-hit descent of the Stelvio climb.
The result was a thorough shake-up to the general classification, with Uran now second to Quintana by 1min 41sec after finishing 4min 11sec behind his Colombian compatriot on the stage.
Evans (BMC), second overall to Uran at the start of the stage, saw his chance to win the Giro effectively end on the final climb of the day as he finished 4min 48sec behind Quintana.
Evans lost the wheel of Uran inside the final five kilometres but remains in a podium position, third at 3min 21sec behind the new race leader.
The day started in some of the most difficult weather conditions imaginable but ended in sunshine on Val Martello and with a new race leader.
With three tough climbs on the menu Uran was always at risk of being put under pressure, and the heavy rain, snow and freezing conditions which prevailed over the Gavia and the Stelvio did little to help.
After Robinson Chalapud (Colombia) soloed off the front early and crested the Passo Gavia first with leader Julian Arredondo (Trek Factory Racing), and Jarlinson Pantano (Colombia) the peloton split apart on the 25km descent to the Stelvio.
The lead group then changed with Dario Cataldo (Sky), Franco Pellizotti (Androni Giocattoli) and Alexis Vuillermoz (AG2R) holding court on the early part of the climb up the Stelvio before they were joined by several other riders.
However it was Cataldo who shook off the break to ride solo to the base of the final Val Martello climb, and as he progressed, Quintana took advantage of the confusion that surrounded news of a possible neutralised descent to slip away from Uran and Evans in a small group.
Organisers later claimed they had simply announced they were placing a motorbike, with a pillion passenger waving a red flag, at the front of the race to warn of any dangers on the road ahead.
Several teams complained after the stage, pointing to a Tweet posted by organisers, and later deleted, that they had understood the race would be "neutralised".
"There was never any question of the race being neutralised,” said race director Mauro Vegni.
After the stage was completed Quintana said he "did not attack" on the descent.
“I don't understand the reasons behind the controversy,” he said. “It was raining a lot, I couldn't see the red flag, all I know is he was supposed to warn us about any dangerous bends."
As the peloton sorted itself into several groups, Quintana was joined by Pierre Rolland (Europcar) and 2012 Giro winner Ryder Hesjedal (Garmin-Sharp) and together the powerhouse trio reeled in Cataldo at the 17km to go mark, with the Uran and Evans group almost two minutes behind.
Sunshine replaced the gloom, and the stage became a ground war between the three men at the front and the chasers behind, with Quintana, Rolland and Hesjedal making clear gains over their pursuers.
The time gap to Uran and Evans grew and Quintana became the virtual leader on the road with 7.7km to go. He chose that same moment to make a final determined push to the finish with only Hesjedal managing to stay on his wheel.
Quintana kept a steady but high pace, and for a moment it looked like Hesjedal would stick with him and perhaps win the stage, however, a final kick by the Colombian was enough to cement the victory, allowing him to pull on the Maglia Rosa for the first time.
Wednesday's 17th stage is a 208km trek over rolling terrain from Sarnonico to Vittorio Veneto.
Stage 16: 139km, Ponte di Legno to Val Martello
1 Nairo Quintana (COL) Movistar 4min 42min 35sec
2 Ryder Hesjedal (CAN) Garmin-Sharp 0:00:08
3 Pierre Rolland (FRA) Europcar 0:01:13
4 Wilco Kelderman (NED) Belkin 0:03:32
5 Domenico Pozzovivo (ITA) AG2R 0:03:37
6 Fabio Aru (ITA) Astana 0:03:40
7 Rafal Majka (POL) Tinkoff-Saxo 0:04:08
8 Sebastian Henao (COL) Sky 0:04:11
9 Rigoberto Uran (COL) Omega Pharma-Quick-Step
10 Cadel Evans (AUS) BMC 0:04:48
1 Nairo Quintana (COL) Movistar 68hr 11min 44sec
2 Rigoberto Uran (COL) Omega Pharma-Quick-Step 0:01:41
3 Cadel Evans (AUS) BMC 0:03:21
4 Pierre Rolland (FRA) Europcar 0:03:26
5 Rafal Majka (POL) Tinkoff-Saxo 0:03:28
6 Fabio Aru (ITA) Astana 0:03:34
7 Domenico Pozzovivo (ITA) AG2R 0:03:49
8 Wilco Kelderman (NED) Belkin 0:04:06
9 Ryder Hesjedal (CAN) Garmin-Sharp 0:04:16
10 Robert Kiserlovski (CRO) Trek Factory Racing 0:08:02
SBS broadcasts every stage of the 2014 Giro d'Italia LIVE! There will be nightly highlights at 5:30pm on SBS ONE, and each stage will also be streamed live here at Cycling Central.
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