It took just four minutes for Liverpool to take the lead in the Premier League encounter when Robin Koch handled the ball and Mohamed Salah scored the resultant penalty.
Leeds were level though in the eleventh minute, with Jack Harrison cutting inside from the left and unleashing a low shot which beat Alisson.
Liverpool went back ahead with 20 minutes on the clock as Virgil van Dijk connected with a corner from Andrew Robertson to direct his header goal-wards, and Illan Meslier could not keep it out.
The game was level once again ten minutes later, Patrick Bamford taking advantage of a mistake from Van Dijk to guide an effort past Alisson.
Liverpool would go in ahead at half time however, with Pascal Struijk not clearing a cross properly and Salah converting from 12 yards out.
But Leeds would not lie down and in the 66th minute, Mateusz Klich combined well with Helder Costa to smash a low shot into the back of the net and make it 3-3.
Liverpool were determined to show champion quality however and when Rodrigo fouled Fabinho in the penalty area in the 88th minute, Salah had a chance to step up and make it 4-3 from the spot, which he did not spurn.
It finished 4-3, handing Liverpool victory to start the defence of their Premier League title.
Reds boss Klopp admits that Leeds caused his side problems and mistakes were made, which he vowed will be worked on, however the Liverpool manager is delighted with the fight his players showed.
“A lot of people said Leeds can cause us problems and they did”, Klopp told the BBC’s Match of the Day.
“We conceded three goals and that means we made some mistakes. They forced us to make mistakes. We have to work on that, we will work on that, and we will be better.
“We were ready for a fight, I like that. I love the desire we showed. We didn’t stop and I like that.
“We will analyse the game. We had mistakes. We have to continue to work. We have to make sure we are prepared next game”, the Liverpool boss added.