After three games, Liverpool top Group C on six points, with two wins and a loss, in a strong position to progress to the tournament's knockout stages.
In an attempts to "avoid any distractions" Xherdan Shaqiri's presence in Belgrade may inspire, Jurgen Klopp opted to leave the Swiss worldwide out of his Liverpool squad for this week's Champions League tie against Red Star.
In team news, there is one major doubt for the Serbian champions is club captain Vujadin Savic.
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.
Milan Pavkov (Red Star Belgrade): Any number of Red Star's defensive shield could lay claim to the award, but it has to go to the man whose two first-half strikes have clinched a famous result. The Reds have to play PSG and Napoli in their final two games, and they'll likely need at least four points to feel good about their chances.
'I think the chances aren't going in for us, we had a number of times in front of goal, times where the goalkeeper saved and times where we weren't on target.
Pavkov rose highest in a crowded penalty area to power home Marko Marin's corner to spark wild scenes of celebration.
Liverpool continued to dominate the ball as Red Star sat back, and Mohamed Salah went close when his 71st-minute effort went behind off the outside of the post.
Salah was nearest to hauling Liverpool back into the game, but Red Star held out for a sensational victory.
Dejan Lovren and Naby Keita have made the travelling party and the former is in line to start while the latter could get a few minutes off the bench in the second half.
"We lost our mojo in the game, not in general. He's our player, he'll play a lot of games for us but not tomorrow".
"We won against a big club and this is a first win in the Champions League for any club in this country and this is why this generation can become equal to earlier generations and enter history".