Liverpool handed Hoffenheim their first home defeat in just over 15 months in a 2-1 victory in Germany this evening.
The reds will bring a one goal advantage back to Anfield for the second leg of the UEFA Champions League playoff next Wednesday.
Klopp picked an unchanged side from the Premier League opening team that were held 3-3 by Watford. Phil Coutinho was still unavailable with his 'back injury'.
Hoffenheim started looking the much stronger side, and Dejan Lovren's defensive abilities were once again called into question. He struggled to deal with a free kick and required intervention by Mignolet to deal with the ball.
And in the 10th minute Lovren's clumsy challenge on Serge Gnabry resulted in a penalty for the home side.
But Andrej Kramaric's penalty was a feeble attempt and Simon Mignolet didn't need to do much to clear it - a let off for Liverpool.
Hoffenheim were controlling possession but the reds were looking dangerous on the counter-attack. In the 34th minute the reds were awarded a free kick when Sadio Mane was charging forward.
From the free kick, 18 year old Trent Alexander-Arnold sent in a curler to the far corner - his first Liverpool goal.
Out for the second half and the home side were looking to get back into the game - Gnabry in particular was a threat for the German side playing their first ever European game.
Roberto Firmino, playing against his old club, should have done better though when Sadio Mane sent over a cross that he only had to beat the keeper with - he fired straight at the number 1.
At the other end Gnabry drilled a powerful shot into the net - but it was ruled out for offside.
In the 63rd minute James Milner came on to replace Jordan Henderson - and the vice-captain would make it 2-0 10 minutes after being subbed on.
Milner received the ball from Firmino and, with the help of a slight deflection, his cross/shot goes over the goalkeeper at the back post. 2-0.
But with 3 minutes remaining Dejan Lovren was involved again - and he played Mark Uth onside from a long ball and the Hoffenheim man grabbed a goal back to give them a chance at Anfield next week.