He scored his first goal in a 4-1 win over Cardiff City last month.
"Then more or less straight away they score the second one and then the atmosphere was completely different, you could feel it". They previously met on October 24, when Liverpool won 4-0 at Anfield.
Nenad Krsticicuels tussles for the ball with Mohamed Salah.
Buvac is still under contract at Liverpool as the Reds continue to negotiate his exit.
Pavkov rose highest in a crowded penalty area to power home Marko Marin's corner to spark wild scenes of celebration. A deflected cross from Liverpool left back Andrew Robertson also bounced onto the crossbar after the break.
Liverpool have only lost one of their last 11 group stage games in the Champions League (W5 D5), scoring 33 goals in total during this run (an average of 3 per game).
Salah nearly sneaked a close-range shot in between goalkeeper and post and Virgil van Dijk headed on to the roof of the net, but there never appeared to be any real threat of them recovering the deficit.
Red Star comes into the match following three straight victories in the Serbian SuperLiga, with the most recent victory coming on the road on Saturday at Proleter Novi Sad by a 2-0 scoreline.
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 Tuesday, but the visitors fell well short of expectations.
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.
Liverpool's performances since the start of the season have seen them tipped as both Premier League and Champions League challengers, but Tuesday's loss will raise fresh questions of continuity.
They got a hard group stage draw when PSG and Napoli came out of the hat with them but they continued their excellent European form with an opening round win against the Ligue 1 champions to put themselves in pole position.
"Maybe if Shaq would have played they (the crowd) go for him or whatever, I don't know, but I didn't think that far", Klopp added.
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