Liverpool went into the game hoping to open up a four-point gap at the summit before Napoli and Paris Saint-Germain faced each other later on Wednesday (AEDT), but the visitor fell well short of expectations.

In the opening 45 minutes, Red Star looked a class apart from the team which lost 4-0 at Anfield two weeks ago, as Pavkov netted twice in seven minutes to leave Jurgen Klopp's side trailing by two at half-time. 

The Premier League outfit's attempts to claw things back saw them hit the frame of the goal twice in the second half through Andrew Robertson and Mohamed Salah, but they were unable to make their pressure tell and Red Star held on to their first win in the group stage.

Liverpool should have had an early lead when Daniel Sturridge inexplicably smashed over from just six yards and Red Star were ruthless in their response.

Pavkov broke the deadlock 22 minutes in with a towering header from Marko Marin's corner after evading the attentions of Virgil van Dijk.

The striker soon got his second, shrugging off Georginio Wijnaldum and beating Alisson with a fierce 25-yard drive to leave Klopp looking stunned on the touchline.

Liverpool had a lucky escape at the start of the second period – the referee failing to award Red Star a penalty when a shot struck the arm of James Milner.

The Reds soon took charge, though their luck in front of goal showed no sign of improving, as a deflected Robertson delivery hit the crossbar and Salah's 72nd-minute effort clipped the outside of the upright.

Salah and Van Dijk then wasted late chances, as Red Star dug deep to open the door to Napoli or PSG in the hunt for first place.