During the summit finish atop the Grand Colombier, Bernal (Ineos Grenadiers) was left far behind and out of the race for the overall win, losing seven minutes and 20 seconds.
Jumbo-Visma set a blistering pace, with Roglič at the helm, however Pogačar (UAE Team Emirates) was the only one able to outmatch him at today's 174.5-km stage, which featured three steep climbs.
The 21-year-old, wearing the young rider leader's white jersey, now sits only 40 seconds behind Roglič and his yellow jersey.
"So far, Roglič has seemed unstoppable; today broke Bernal, perhaps on another day, it will be me or Roglič. We can't know that for sure," said Pogačar, who is now the youngest rider to have bagged two stage wins in the past 86 years of the race, according to RTV Slovenija data. He also vowed to keep up the pace.
Roglič meanwhile thanked his team and pointed out that the key stages were yet to come. "It would have been good if I had gained four seconds, but I was too short and Tadej was too good today. Nevertheless, I'm satisfied," said Roglič, who will don the yellow jersey for the seventh time on Tuesday.
Colombian Rigoberto Uran (EF Pro Cycling) ranks third in the overall standings, with a minute and 34 seconds between him and Roglič.
The 30-year-old became the first Slovenian ever to claim the leader's jersey of the most prestigious cycling race in the world a week ago.
This is also the first time ever that two Slovenian competitors top the overall rankings at the Tour.
Monday will be a rest day for the riders and a third series of coronavirus tests will be performed.