Navardauskas, who rides for the Garmin-Sharp squad, clocked 4 hours, 23 minutes, 14 seconds over the 182-kilometer (113-mile) leg from Tarvisio to Vajont, which featured two category-2 climbs, including an uphill finish.
Italians Daniel Oss and Stefano Pirazzi finished second and third, respectively. Oss crossed 1 minute, 8 seconds behind and Pirazzi was 2:59 back.
Nibali, an Italian with Astana, maintained a 41-second lead over 2011 Tour de France winner Cadel Evans, as the top of the overall standings remained unchanged.
The stage was held in conjunction with the 50th anniversary of the Vajont dam disaster, which killed nearly 2,000 people and devastated the area on Oct. 9, 1963.
Meanwhile, the race's first doping case came as the UCI notified French rider Sylvain Georges that he tested positive for a banned stimulant.
Stage 12 Thursday is a 134-kilometer (83-mile) leg from Longarone to Treviso that starts with a few hills before a long, flat finish.
The race ends May 26 in Brescia.