Five days after his team-mate Jack Bauer was caught by the peloton a few metres from the line after a 222-km breakaway, Lithuania's Navardauskas attacked on a short climb close to the finish and never looked back.
German John Degenkolb took second place, seven seconds behind, and Norway's Alexander Kristoff finished third after the main bunch was split by a late crash. All the riders from the main pack were credited with the same time as the incident happened with less than three kilometres left to run.
"I was the first to crash, I did not know what happened," said Slovakian Peter Sagan, who had been tipped as one of the stage favourites.
Nibali still leads Thibaut Pinot of France by 7:10 and another Frenchman, Jean-Christophe Peraud, one of those who crashed, by 7:23, ahead of today's decisive time trial. That comprises a 54-km solo ride between Bergerac and Perigueux.
Garmin-Sharp, without team leader Andrew Talansky after the American pulled out due to lower back pain, had only a stage win in mind. They had Tom-Jelte Slagter in the day's breakaway and the Dutchman served as a launchpad for Navardauskas after the climb.
"The plan was to attack in the climb and to have one of our riders in the breakaway so he could take a strong relay to help me," said Navardauskas. "It's almost amazing to keep the peloton at bay. Until the last 10 metres I was afraid to turn back."
Navardauskas powered away from the pack on the fourth-category climb of the Cote de Monbazillac, 13km from the finish. Pinot's FDJ.fr team led the peloton in the descent and on the flat portion leading to the line, with Cannondale and Tinkoff-Saxo chasing the Garmin-Sharp rider who was 25 seconds ahead with five kilometres left.
With just under three kilometres remaining, Peter Sagan was involved in the crash as well as France's Romain Bardet who is fifth in the overall standings. "We knew it would be a nervous stage. I did not crash, it's all good," said Pinot.