Liverpool spoiled Hoffenheim's debut in European competition by winning 2-1 in the first leg of their Champions League playoff on Tuesday.
Liverpool goalkeeper Simon Mignolet had already saved a weak penalty from Andrej Kramaric by the time 18-year-old right back Trent Alexander-Arnold curled a kick over the wall and into the bottom right-hand corner from about 30 meters (yards) in the 35th minute.
"Our little hero," Liverpool manager Juergen Klopp said of Alexander-Arnold, who has been at the English club since the age of 6, has played for England's youth teams and is making his full breakthrough in the first team this season while Nathaniel Clyne is injured.
It was his first goal for the club, on his ninth start.
"The free kick is no coincidence, he's been doing that every day in training," said Liverpool midfielder Jordan Henderson, one of a number of senior players who are happy to hand over free kicks and corners to the teenager. "Now he's done it on the big stage."
Havard Nordtveit inadvertently deflected substitute James Milner's cross from the left high into his own net to put the five-time European champions 2-0 up in the 74th minute.
However, substitute Mark Uth gave Hoffenheim a glimmer of hope going into next week's second leg at Anfield when he chested down a long ball forward and drilled an angled shot into the corner in the 87th.
Liverpool is looking to become the fifth English team to qualify for the group stage — joining Chelsea, Tottenham, Manchester City and Europa League winner Manchester United — and return to Europe's top competition for the first time since the 2014-15 season.
Hoffenheim is in unknown territory after reaching the Champions League playoffs courtesy of a fourth-place finish under Julian Nagelsmann, its 30-year-old coach. It was the highest-ever finish by the team from a village of around 4,000 people in southwest Germany.
In other first-leg results, CSKA Moscow benefitted from an own goal in second-half injury time to beat Young Boys 1-0, Azerbaijani team Qarabag beat FC Copenhagen 1-0, and APOEL Nicosia won 2-0 at home to Slavia Prague. Sporting Lisbon and Steaua Bucharest drew 0-0.