Milan Pavkov took full advantage of Liverpool mistakes to net a first-half brace, and the hosts produced an obdurate defensive display in the second half to keep last season's runners-up at bay just a fortnight after being swept aside at Anfield.
Liverpool remain top of Group C despite the result, but they are only a point clear of Napoli and two above Paris Saint-Germain, who face each later today and provide the final two opponents for Jurgen Klopp's side in the group stages.
Red Star, meanwhile, are still bottom of the group but move level on points with PSG ahead of tonight's match courtesy of their first ever victory in the Champions League proper.
Red Star's supporters were banned from attending the heavy defeats at Paris Saint-Germain and Liverpool on matchdays two and three, but they created a hostile environment from the very first whistle and were encouraged by early sights of goal for Nenad Krsticic and Marko Marin.
The first clear chance fell the way of Red Star's skipper Vujadin Savic when the ball fell to him inside the penalty area, but he failed to keep his shot down on the turn.
Liverpool's struggle to deal with the Red Star corners would cost them eventually, but only after Liverpool had missed a glorious chance to break the deadlock when Daniel Sturridge - chosen ahead of Roberto Firmino - blazed the ball over the bar with the goal gaping from just six yards out.
Sadio Mane's pace was beginning to cause the hosts problems and he slid the ball through for Sturridge again moments later, only for the striker to cut back and see his eventual effort deflected wide for a corner.
Red Star responded by drawing the first meaningful save from Alisson Becker as he turned El Fardou Ben Nabouhane's long-range snapshot around the post, and that proved to be a warning for the visitors as the hosts took the lead from the resulting corner.
Liverpool's defenders failed to block the run of Pavkov, who rose unchallenged before planting a towering header past Alisson to raise the decibel levels even further inside the stadium.
It was the striker's first ever European goal for the club, and it took just seven minutes for him to add a second, too. James Milner gave the ball away inside his own half, and Pavkov proceeded to shrug off the challenge of Georginio Wijnaldum before firing a powerful 25-yard strike into the corner.
Liverpool were made to rue a catalogue of errors in the buildup to the goal once again, with questions raised over Virgil van Dijk, Joel Matip and Alisson as Klopp's side found themselves with a mountain to climb after half an hour.
The visitors almost responded quickly with Mohamed Salah firing a first-time volley over before Wijnaldum and Adam Lallana both saw goalbound headers blocked before they could test Milan Borjan in the Red Star goal.
Sturridge then fired off target at the end of a jinking run when the better option was to pass it, and the striker was one of two players to pay for Liverpool's poor first-half performance when Klopp made changes at the break.
Firmino and Joe Gomez were brought on for Sturridge and Trent Alexander-Arnold, but Liverpool were immediately on the back foot at the start of the second half too and survived a couple of early scares in the opening minutes.
The visitors did create another clear chance to get themselves back into the game shortly after the restart themselves, though, when Firmino's deflected cross fell to Mane, who could not prod the ball home from close range.
Not much was going the way of Liverpool in the final third, and the woodwork came to Red Star's rescue 11 minutes into the second half when Andrew Robertson's cross took a big deflection before looping over the keeper and onto the top of the crossbar.
Klopp's side dominated possession throughout the second half, but the home side looked like a different proposition to the one which had conceded 10 times in their previous two Champions League games as they kept the five-time winners at arm's length.
Salah did almost force a breakthrough when he saw one deflected shot tipped wide by Borjan before picking up the loose ball from the resulting corner and releasing a smart volley which clipped the outside of the post.
Red Star's packed penalty area saw space at a premium for Liverpool's attackers, and both Salah and Firmino failed to get a good shot away during a mini-scramble before Matip should have done better with a header from Gomez's long throw.
Van Dijk also sent a header looping onto the roof of the net as the hosts refused to give anything away, and by the time the fourth official indicated five minutes of stoppage time it was clear that Liverpool would not get back into the match.
There was a chance for a late consolation when the ball broke kindly for Salah in the area, but his finish - and Borjan's celebrations at saving it to keep his clean sheet intact - summed up a famous night for Red Star and one to forget for Liverpool.
RED STAR (4-2-3-1): Borjan; Stojkovic (Gobeljic 59'), Savic, Degenek, Rodic; Jovancic, Krsticic (Jovicic 73'); Ben, Marin (Causic 64'), Srnic; Pavkov
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold (Gomez 46'), Matip, Van Dijk, Robertson; Milner, Wijnaldum, Lallana (Origi 79'); Salah, Sturridge (Firmino 46'), Mane