The burly frontman gave the hosts a shock lead at the Rajko Mitic Stadium as he headed home a corner in the 22nd minute before showing he has much more in his locker than brute strength just six minutes later.
Picking the ball up just inside the Liverpool half, the 6'4" striker drove forward before unleashing a howitzer of a strike from 25 yards.
Alisson in the Liverpool goal had no answer to the effort and could only watch as it blitzed past his outstretched hand and into the top corner.
It was a fine way for Pavkov to mark his first start in the Champions League this season as Red Star looked to keep their Champions League hopes alive.
The goals take the 24-year-old to seven in 17 games in all competitions so far this season.