Pogacar now leads by two minutes and 42 seconds from his main rival Jonas Vingegaard, who finished second on the 186km Pyrenean stage from Pau to Gavarnie-Gedre to move up to second overall.
Pogacar's team-mate Isaac Del Toro beat Remco Evenepoel in the sprint for third to leapfrog the Olympic champion in the standings for third overall at 3:27.
Norwegian Torstein Traeen had started the day in yellow, but he lost contact with the lead group before the halfway point of the punishing Tourmalet climb with around 50 kilometres still to ride, and from then on it was clear that his grip on the jersey was gone.
To make matters worse, he crashed on the descent - his second spill in as many days.
Pogacar's UAE Emirates-XRG team ramped up the pace on the two Pyrenean behemoths, the Col d'Aspin and Col du Tourmalet, on another scorching day in southwestern France where temperatures again hit 40C.
The world champion attacked about 4km from the summit of the Tourmalet and he quickly gapped his rivals.
At the summit, Pogacar led Vingegaard by 30 seconds with Paul Seixas, Florian Lipowitz and Del Toro another minute behind.
Other contenders Evenepoel and Juan Ayuso were in a small group a further 20 seconds back.
On the descent and then the final long but gentle climb to the finish, Pogacar gradually extended his lead, all but suffocating any hope of his rivals challenging him for the overall victory this year.
Vingegaard battled to limit his losses while behind him the two chasing groups merged but failed to cooperate effectively.