Roberto Firmino came off the bench to strike deep into stoppage time and hand Liverpool a deserved 3-2 win over Paris Saint-Germain at Anfield on Tuesday.
Last season's finalists showed the French champions have plenty of work to do if they are to mount a challenge for a first-ever Champions League title as they bounced back from blowing a 2-0 first-half lead.
Daniel Sturridge and a James Milner penalty put the hosts in command before Thomas Meunier reduced PSG's arrears.
Having kept Kylian Mbappe and the world's most expensive player Neymar quiet for almost the entire match, Liverpool seemed set to pay a heavy price for one slack pass by Mohamed Salah as Mbappe swept home seven minutes from time in front of a stunned Kop.
But Firmino, who started on the bench due to an eye injury suffered against Tottenham on Saturday, had the final say as he twisted and turned before firing into the far corner to stretch Liverpool's perfect start to the season to six games.
Liverpool's run to the final last season was characterised by fast starts that blew away Spartak Moscow, Manchester City and Roma at Anfield and buoyed by a perfect start to the Premier League season, the hosts put PSG under severe pressure from the off.
Alphonse Areola has kept Gianluigi Buffon on the sidelines during the first few weeks of the 40-year-old's PSG career and, with the Italian suspended for his red card in Juventus' controversial exit to Real Madrid in the quarter-finals last season, started again between the sticks.
The French international was busy early on as he saved from Virgil van Dijk, Milner and Sadio Mane inside the first 10 minutes.
PSG have crumbled on their Champions League travels to Barcelona, Bayern Munich and Real Madrid in the past two seasons and their ability to challenge for the competition was again questioned as they struggled to contain Liverpool's greater speed and power in midfield.
Up front, Firmino's absence opened the door for Sturridge to make his first Champions League start for the club.
The Englishman has been dogged by injury and lack of form during Klopp's nearly three years in charge, but took his chance on the big stage by powering home a pinpoint curling cross from Andy Robertson to open the scoring on the half-hour mark.
Six minutes later, PSG's deficit was doubled when Juan Bernat tripped Georginio Wijnaldum inside the area and Milner slammed the resulting penalty into the bottom corner.
However, the visitors were handed a lifeline through right-back Meunier, rather than one of their famed front three, as the Belgian skilfully readjusted to volley home Robertson's miscued clearance.
Klopp was annoyed at his side for having to survive a nervous finale in winning at Tottenham on Saturday after passing up a series of chances to put the game to bed.
And it was looked like this time they would pay as Salah had a goal ruled out for a foul by Sturridge before the latter headed a glorious chance into the arms of Areola.
Salah has struggled to match his stunning 44-goal form of last season in recent weeks and was substituted by Klopp moments after gifting PSG a route back into the game.
His slack pass was intercepted and quickly fed into Neymar, with Van Dijk's tackle on the Brazilian only rebounding into the path of Mbappe to fire home.
Liverpool instantly went in search of a winner as Trent Alexander-Arnold's deflected free-kick came back off the woodwork, and finally got their reward when Firmino powered home.