Pre-race favourite Bradley Wiggins dropped further behind on the steep, uphill finish, while defending champion Ryder Hesjedal dropped out of contention on the first climb.
The 26-year-old Uran, who rides for Wiggins' Sky team and won the best young rider's jersey during last year's race, clocked more than 4 1/2 hours over the 167-kilometre leg from Cordenons to Altopiano del Montasio, which featured two difficult climbs, including a long, grueling uphill finish.
It was Uran's first victory in a Grand Tour.
"It nice to finally be able to finish off a victory," he said.
Another Colombian, Carlos Betancour, finished 20 seconds behind in second. Nibali, an Italian with Astana, won a sprint for third, 31 seconds back to keep the pink jersey.
Mauro Santambrogio was fourth and 2011 Tour de France winner Cadel Evans crossed fifth, both also 31 seconds back.
Wiggins crossed 10th, 1:08 back.
Victoria's Hesjedal was 71st in the stage, 20 minutes 53 seconds behind Uran. He dropped to 33rd overall, 23:45 behind Nibali.
Nibali earned an eight-second bonus for finishing third and increased his lead over Evans to 41 seconds. Uran moved up from ninth to third, 2:04 back. Wiggins remained fourth but now trails by 2:05, while Robert Gesink of the Netherlands is fifth, 2:12 behind.
Michele Scarponi, the 2011 Giro winner, dropped from fifth to sixth.
"Today could have been a difficult day because it followed a rest day," Nibali said. "Wiggins lost some time. I was worried about Scarponi, but he also lost something. At this point, I think Evans becomes one of the most dangerous opponents.
"I have a decent lead on Uran and just as much on Wiggins. I think we'll keep an eye on both of them. I won't know Sky's strategy but we'll try to figure it out."
Henao, another strong Colombian climber for Sky, is 19th overall.
"We had three cards to play — me, (Sergio) Henao and Wiggins — and it worked for me today," Uran said. "We have the strongest team. ... Both Henao and I know that our job is to help Bradley. But then of course we'll see day by day what happens."
The first climb over the Cason di Lanza pass lasted 14.5 kilometres at gradients as high as 16 per cent with snow lining the road. The finishing climb to Montasio, in the Giro for the first time, lasted 21.9 kilometres with leg-breaking stretches at 20 per cent gradients.
Earlier this year, fans were allowed to send in messages for the stage via Twitter, which were printed on the road leading up to Montasio, which is located in the northeastern corner of Italy.
The stage began with a 13-man breakaway, which fell apart on the first climb. Nibali had a tire puncture but quickly caught back up to the main pack with the help of his teammates.
On the finishing climb, Sky rode up front to set up Uran's attack with eight kilometres to go.
Before Tuesday's start, German sprinter John Degenkolb withdrew. He won the fifth stage.
Stage 11 Wednesday is a 182-kilometre leg from Tarvisio to Vajont featuring two category-2 climbs.
The race ends May 26 in Brescia.