Navardauskas dropped fellow escapee Daniel Oss (BMC) on the second of two climbs with 5km remaining of the 182km stage from Tarvisio to Vajont to set up the biggest win of his career.
The 25-year-old all-rounder - who became the first Lithuanian to don the fabled maglia rosa after Garmin's victory in the team time trial in his debut Giro last year - finished 1min 08secs ahead of Oss after a largely uneventful day in the 96th edition of La Corsa Rosa.
There was no change in the overall standings after all the race favourites came home in the main pack more than five minutes down on Navardauskas, the third Lithuanian to win a stage on the Giro.
Victory for Navardauskas comes as a tonic to his Garmin team, whose leader Hesjedal cracked in the mountains on Tuesday's stage 10 to lose almost 21 minutes and end any lingering chances of retaining his Giro crown.
"Since yesterday our plans changed because Ryder had a bad day. From today we had different tactics and the plan was to get in the breakaway," an ecstatic Navardauskas told Eurosport.
"But the stage started with a downhill and tailwind and it was very hard to get into the break."
Indeed, with a blistering average speed of 53.5km/h set over the first hour and a half of racing, it took until the 82nd kilometre before a group formed off the front of a fast-pedalling peloton.
Once established, the 20-man group - which contained riders from every team except Lampre-Merida, Lotto Belisol and the Astana outfit of race leader Nibali - quickly built up a maximum lead of six minutes over the peloton.
Stefano Pirazzi (Bardiani Valvole) attacked from the break near to the summit of the Cat.2 Sella Ciampigotta climb in a bid to consolidate his lead at the top of the mountains competition.
The Italian was denied maximum points by Venezuela's Jackson Rodriguez, who was riding off the front of the race for a second day running. The pint-sized Androni Giocattoli rider moved into second place in the blue jersey competition with his haul.
German powerhouse Patrick Gretsch attacked his fellow escapees on the long, sinuous descent. The Argos Shimano rider managed to build up a lead of 1:45 over the chasing group but was finally reeled in with 18km remaining after Navardauskas and Oss had taken matters into their own hands and attacked the other fugitives.
Gretsch soon cracked as the road started to head back uphill - and once the final 7km ascent to the finish line was reached by the leading duo, Navardauskas shed sprinter Oss with apparent ease to solo up the slope to glory.
The stage finished nearby the old Vajont Dam where tragedy struck fifty years ago when a landslide killed more than 2,000 people in the Pieve Valley.
With Navardauskas sure of the stage victory, Pirazzi attacked from the chasing group to take third place, just under three minutes behind the winner. The Italian added more KOM points to his tally to open up a 20-point lead over Rodriguez in the battle for blue.
Former race leader Salvatore Puccio of Team Sky crossed the line for fourth place, 3:07 down on Navardauskas as the remnants of the initial break arrived in dribs and drabs at the summit.
Spain's Benat Intxausti - another rider who donned the pink jersey for just one day earlier in the race - attacked the main pack on the final descent to take 20th place. The Movistar rider moves back into the top ten, 4:05 behind Nibali on GC.
Sicilian Nibali leads Australia's Cadel Evans, the red jersey from BMC, by 41 seconds with Colombian Rigoberto Uran in third place, 2:04 down and one second ahead of British Sky team-mate Bradley Wiggins, in fourth.
Frenchman Sylvain Georges of Ag2R-La Mondiale did not start stage 11 after voluntarily withdrawing from the race following a positive test for the stimulant Heptaminol.
Georges, 28, returned the positive test in a urine sample collected after stage seven of the race, on 10th May 2013.
The race continues on Thursday with the short 134km stage 12 from Longarone to Treviso, which looks destined to give the sprinters a rare chance to shine.