Egypt's Mohamed Salah was on target as Liverpool convincingly defeated Hoffenheim 4-2 at Anfield on Wednesday to reach the Champions League group phase for only the second time since 2010.
Germany midfielder Emre Can found the net twice in the opening 21 minutes, either side of Salah's first Anfield goal following his move from Roma, before substitute Mark Uth replied for the visitors.
Hoffenheim old boy Roberto Firmino netted a fourth goal in the second half and Sandro Wagner's late header proved anecdotal as Jurgen Klopp's men completed a 6-3 aggregate victory.
Now unbeaten in 15 home games against German teams, Liverpool will learn their group-stage opponents in Thursday's draw in Monaco, which will feature five English clubs for the first time.
Liverpool join Chelsea, Tottenham Hotspur and Manchester City, who qualified via the Premier League, and Manchester United, who engineered their own Champions League return by winning last season's Europa League.
Liverpool will be making their first appearance in the Champions League proper since 2014-15, when they were eliminated in the group stage.
Klopp was once again without Barcelona target Philippe Coutinho, who is both ill and nursing a sore back, but the sizzling interplay of Firmino and Sadio Mane meant he was not missed.
The five-time European champions took a 10th-minute lead against continental first-timers Hoffenheim courtesy of the first of several delightful interchanges between their forward players.
Firmino's delicately weighted through-ball freed Mane and he back-heeled the ball into the path of Can, whose shot found the net via a heavy deflection off the sliding Havard Nordtveit.
Egyptian winger Salah struck in the 18th minute, tapping in from close range after Georginio Wijnaldum's shot from Firmino's left-wing cut-back bounced back off the right-hand post. It was his second competitive goal since he joined this summer.
Three minutes later another Mane back-heel yielded another goal, the Senegal winger's touch releasing Firmino, whose cross was adroitly volleyed home by Can.
Hoffenheim coach Julian Nagelsmann took swift action, sending on forward Uth for defender Nordtveit, and four minutes later Dejan Lovren's loose pass allowed the substitute to reduce the arrears with an angled drive.
After Wijnaldum and Mane had gone close, Liverpool added a fourth in the 63rd minute when skipper Jordan Henderson robbed his Hoffenheim counterpart Kevin Vogt and charitably teed up Firmino for a tap-in.
Wagner completed the scoring with a header from Andrej Kramaric's left-wing cross, but by then all hope of a Hoffenheim comeback had vanished.