The stage finished among cheering crowds, many waving Slovenian flags, and the snow-covered peaks surrounding Livigno, at a height of just under 2,400 metres.
Pogačar powered to victory, 29 seconds ahead of former Giro winner Nairo Quintana of Colombia.
Tarmac on some parts of the road up to the summit finish had only been laid yesterday.
Afterwards, Pogačar paid tribute to Quintana and Germany's Georg Steinhauser, who came third.
He said that his UAE Emirates team had done a good job and had been thinking about the stage since December. He added that Livigno happened to be one of his favourite places in Italy.
It has been an almost perfect weekend for the world no.1 cyclist, who came 2nd in a relatively flat time trail yesterday to Italy's time trail expert Filippo Ganna.
Pogačar now has a lead of 6 minutes and 41 seconds over his nearest rival, last year's runner-up, Geraint Thomas of Wales. He has also extended his lead in the overall standings for the Maglia Azzurra, or Blue Jersey, which goes to the best climber.
Tomorrow is a well-earned rest day for the riders before the final week of the year's first Grand Tour. There are still four more mountain stages to go before the peloton crosses the finish line for the final time this year in Rome next Sunday.
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