Defending champion Bernal and France's Pinot were seemingly content to maintain their pace as the Slovenian powered to victory and claimed a 10-second bonus.
The effort came at the end of the 7.1-km ascent to the ski resort of Orcieres-Merlette, the first uphill finish of this year's Tour.
Roglič, who has been in ominous form this season, is confident he can sustain his level.
"I feel every day a little better. It's still not totally the same but I got confirmation in the second stage (in the mountains) that I could still ride a bike," Roglič said.
"We just have to stay focused and do the same."
Bernal grimaced during the ascent and Pinot, who usually enjoys sprints at the end of climbs, was content with finishing eighth, a spot behind the Colombian.
The 30-year-old Pinot, carrying France's hopes of a first home winner on the Tour since Bernard Hinault in 1985, sustained bruises on the opening stage and he has yet to fully recover.
"To be honest, after what happened on Saturday, we're really happy to be where we are," Pinot's sports director at Groupama-FDJ, Philippe Mauduit said.
The Frenchman, who has worked with Tour champions Alberto Contador and Vincenzo Nibali during his career, believes Roglic might not even be the most dangerous man in the race.
"The truth of the first week is rarely the truth of the third week on the Tour," he said.
"And to be honest maybe I'm more scared of (Roglič's team mate) Tom Dumoulin than of Roglic."
Dutchman Dumoulin, who won the Giro d'Italia in 2017 and ended up second in the 2018 Tour, took a tumble on Sunday but his form has been improving lately.
If Roglic has peaked too early, he will be Jumbo Visma's main weapon.
"Handling the pressure of leading the Tour is also something very hard," Mauduit said.
Pinot said last week that he was feeling stronger than last year when a thigh injury forced him to abandon the race while he was battling it out for victory with Bernal.
If so, he will be able to do some damage on the longer climbs, along with the defending champion.
"I think we need to be patient and our best scenario is to arrive in the third week without losing too much time," Bernal said.
"And then we'll try to recover a bit of time in the long climbs, try to arrive as fresh as we can in the last week."