The Garmin-Sharp rider became the first Lithuanian to win a stage of the Tour, coming home seven seconds clear after a rain-soaked day's cycling from Maubourguet Pays du Val d'Adour to Bergerac.
Navardauskas mounted an attack in the final 15 kilometres, moving ahead in the climb towards the finish line as none of the chasing pack were able to stay with him.
And afterwards, Navardauskas revealed that those tactics had been in place from the start of the 208.5km stage.
"This was the plan from the beginning," he said. "To have someone in the break.
"If we didn't we had to work on the final climb. Thankfully Tom [-Jelte Slagter] was in the break. He did an amazing job.
"And then he had the strength to help me on the top. That gave me some extra motivation. I didn't want to disappoint my team-mates. I am really happy for the team."
There was a heavy crash towards the stage's conclusion, as a number of riders went down - including points leader Peter Sagan (Cannondale) - but as the accident happened within the final 3km there were no time implications for any riders.
"I don't really know what happened," said AG2R-La Mondiale's Romain Bardet.
"Some riders fell in front of me and I couldn't avoid them, and lots of us hit the ground. But it's okay. I'm not in much pain."