The pair had been part of a five-man group who broke from the main pack on the day's final climb, with 13km left of a 256km slog over 11 tough climbs in the Ardennes.
The Slovene Pogacar, the French riders Julian Alaphilippe and David Gaudu, the Canadian Michael Woods and the Spanish veteran rider Alejandro Valverde broke away from the rest of the peloton at the top of the Roche-aux-Faucons climb.
It then became at cat and mouse affair through the countryside just outside Liège. Valverde broke for the line early and was overhauled by Alaphilippe and Gaudu with just 50 metres to go. However, 22-year-old Pogacar found fresh energy and came from the back at lightning pace to seize victory right on the line.
Speaking after the race Tadej Pogacar told journalists "I sat on Alaphilippe's wheel in the run-in. I knew he could go for it from distance and I just managed to get him".
Speaking about the oldest one-day spring classic
the Slovene rider said. "I love this race".
Demi Vollering wins women’s race
Earlier on Sunday, the Dutch rider Demi Vollering won the women's race ahead of another Dutch rider Annemiek van Vleuten and the Italian rider Elisa Longo Borghini.
The women's 140km race runs from Bastogne to Liège and takes in seven hills along the same narrow and winding Ardennes forest roads as the men’s race.