Pogacar (UAE Team Emirates) attacked with 34km remaining of the 254km trek as the field tackled the iconic Cote de la Redoute and he then surged clear.
He finished one minute 39 seconds ahead of Romain Bardet while Dutchman Mathieu van der Poel won a sprint to claim third.
It was the second Liege victory for Pogacar and made up for last year when he crashed. He also departed the 2022 edition of the race after the death of his fiance's mother.
"It was quite emotional for me all day riding on the bike, thinking of Urska's mother two years ago and we had to go home," Pogacar said. "Then last year when I broke my hand so the last two years were really difficult."
Pogacar said the plan to attack on the Cote de la Redoute had been worked out before the race.
"We rode hard on the climbs, and safe on the downhills and on La Redoute - we did exactly what we said and from then on it was suffering to the finish," he said.
