Liverpool got their Champions League campaign off to a flyer as they ended Hoffenheim's 15-month unbeaten run at home to take two away goals from the Rhein-Neckar-Arena.
Things could have been so different for the hosts had Andrej Kramarić converted his 12th minute penalty, but the Croatian struck tamely and straight at Simon Mignolet before Trent Alexander-Arnold's first Champions League goal opened the scoring.
James Milner's cross deflected in off fellow substitute Håvard Nordtveit 15 minutes from time to wrap up the game and give Liverpool two precious away goals heading into next week's second leg at Anfield despite Mark Uth's late consolation.
Unchanged side proves to be the key for Klopp
Julian Nagelsmann made six changes from their DFB Pokal win at FC Rot-Weiß Erfurt on Saturday as Nadiem Amiri, Jeremy Toljan, Gregor Kobel, Nordtveit, Nico Schulz and Eugen Polanski made way for Oliver Baumann, Pavel Kadeřábek, Lukas Rupp, Steven Zuber, Benjamin Hübner and Serge Gnabry.
Jürgen Klopp meanwhile fielded the same side that drew 3-3 at Watford in Saturday's Premier League opener, handing 18-year-old right-back Alexander-Arnold his Champions League debut.
Achtzehn99 made what they thought was a dream start to their first ever Champions League fixture 11 minutes in as on-loan winger Gnabry evaded Alberto Moreno on the right flank, before faking one way and heading the other against Dejan Lovren who clumsily tripped the German for a penalty.
Former Leicester City forward Kramarić stepped up to the spot and took an all too casual run up before placing straight at the Reds' goalkeeper Mignolet, wasting Hoffenheim's chance to make a huge statement so early on.
Then, on 35 minutes, Ermin Bičakčić gave away a free-kick 25 yards away from goal and received a booking for his troubles although that was soon to be the least of his worries.
German international Emre Can stood over the ball and was expected to be the man aiming at goal but youngster Alexander-Arnold had other ideas, curling the ball around the wall and into the bottom corner to open the scoring and leave Baumann rooted to the spot.
Both sides had big chances to score before the break as Gnabry picked up a long ball just inside the Liverpool box and saw his shot saved by Mignolet, before Sandro Wagner fired the rebound off the post with the goal gaping.
Lovren almost got on the scoresheet in added time from a corner kick, his header skimming the far post as referee Björn Kuipers signalled for half-time.
Late consolation offers hope for Hoffenheim
Chances continued to formulate at both ends with Gnabry volleying over from Wagner's cross while at the other end Mohamed Salah saw his shot saved from an acute angle.
The Reds found that crucial second goal deep into the second half as substitute Milner was found by Roberto Firmino's defence splitting pass, before his cross deflected off Nordtveit and into the top corner.
Controversy surrounded Liverpool's second as Baumann and other Hoffenheim players complained that the quick free-kick taken in the build up to the goal was taken from the wrong position in addition to the ball being mobile, but their complaints did nothing to change the two-goal deficit.
Uth instead used his feet to change the deficit three minutes from time as Alexander-Arnold was caught sleeping on the right side, allowing the German to drift in behind before taking two touches to chest and finish.
Hübner should have equalised in added time as he got on the end of a wide free-kick and headed over the bar from eight yards out, leaving fans to ponder what could have been.
The Bundesliga side still need two goals at Anfield to progress to the group stage, but their late show proves they can rattle the Liverpool backline enough to cause problems.