Intxausti won in a time of 5 hours, 52 minutes, 48 seconds, along the hilly 238 kilometres (148 miles) from Valloire, France, to Ivrea beating Tanel Kangert and Przemyslaw Niemiec in a final sprint.
Nibali, who finished third and second in his last two Giro d'Italia races, maintained his lead of 1 minute, 26 seconds over Cadel Evans and remains firmly on course to win his country's biggest cycling race for the first time.
Mauro Santambrogio started the day fourth but lost more than two minutes to slip to sixth.
Taylor Phinney was forced to retire midway through the stage due to saddle sores. The American had hoped for a stage win, while also working for team leader Evans.
Intxausti, who briefly wore the leader's pink jersey in the race, moved up to ninth.
"Today I can really say I enjoyed it," Intxausti said. "It seemed like the least appropriate day for me because the breakaway group looked like it was going to make it to the finish, and that makes it even more beautiful and special. The main favourites looked to each other on the downhill, and I took advantage of that to escape.
"I knew Kangert was the most dangerous rider because he was always on my wheel. I kept my mind cold in the final kilometre and left all responsibility to Niemiec. I saw them glancing for a bit with 250 metres to go and I didn't wait, I jumped from the left side ... and it all went well. As soon as I crossed the line, I screamed with fury and emotion."
Intxausti dedicated the victory to former teammate Xavier Tondo, who died in May 2011 after being crushed by his garage door as the duo were preparing to go on a training ride.
Monday was a rest day following two tough mountain stages in atrocious weather conditions.
The stage started in France and, following several early attacks, a group of 16 finally broke away to climb Mont Cenis and build a lead of three minutes. The group increased to 22 riders as they crossed back into Italy after 78 kilometres (48.5 miles).
The leading group held an advantage of more than five minutes, but the peloton upped its pace and the gap started dropping rapidly with 65 kilometres (40 miles) remaining.
Several riders tried to attack from the front of the lead group but they were caught as the advantage over the peloton continued to fall.
Wilco Kelderman, Emanuele Sella and Danny Pate led by more than 1 1/2 minutes heading into Ivrea, ahead of the circuit around the town and the final climb. They were caught by a group of five with 25 kilometres (15.5 miles) to go.
Carlos Betancur attacked 18 kilometres (11 miles) from the finish as he rode the final climb up to Andrate, but that sparked a chase from Nibali followed by most of the other favourites.
There were several small attacks at the front, but nothing significant until Niemiec, Kangert, Intxausti and Robert Gesink carved out a small advantage.
However, disaster stuck for Gesink 1.8 kilometres (1.12 miles) out as he dropped back with a mechanical problem, leaving the other three to battle it out.
They watched each other closely as they approached the finish. Niemec was the first to attack, but he made his move too early and was swiftly passed down the left by Intxausti, who held off Kangert.
Wednesday's 17th stage is a flat 254 kilometres (158 miles) from Busseto to Cherasco. It could be ideal for Mark Cavendish — who celebrated his 28th birthday on Tuesday — to claim a fifth victory in this year's race.
The Giro ends May 26 in Brescia.