Emre Can netted either side of a Mohamed Salah strike as the Reds made a blistering start to proceedings on the long-awaited return of European nights at Anfield.
The Germans reduced the deficit shortly before the break when early substitute Mark Uth produced a clinical finish from what was a rare chance for the visitors in a one-sided 45 minutes.
But a less frantic second half saw Roberto Firmino tap in following good work from Jordan Henderson and effectively put the seal on Liverpool's return to Europe's elite cup competition despite Sandro Wagner's late header.
The key points…
- Reds race into three-goal lead
- Can (two) and Salah net in first 20 minutes
- Uth pulls one back before half-time
- Firmino goal in second half seals it
- Wagner heads in late consolation
The team news…
Having made five changes for the weekend win over Crystal Palace, Jürgen Klopp reverted to the starting XI that had previously earned victory at Rhein-Neckar-Arena.
However, unlike in Germany, Andy Robertson and Daniel Sturridge took up two of the places on the substitutes' bench.
The first half…
The Reds wasted little time in signalling their intent, going close in the opening moments through a Salah header and a Sadio Mane one-on-one that was well saved.
As such, it was little surprise to see the opener come after just 11 minutes - and not until after Serge Gnabry had looked certain to score from what transpired to be an offside position.
It came courtesy of Can, whose overlap was rewarded with a well-timed tee-up from Mane and a slight deflection on his side-footed finish.
The midfielder's intricate link-up with Alberto Moreno and Firmino was also key to the second, and resulted in the latter teeing up Gini Wijnaldum for a shot onto the post that was touched in by Salah.
And it was dreamland for the Reds in the 21st minute as Firmino's stand-up to the back post was met emphatically by Can to make it 3-0.
Hoffenheim coach Julian Nagelsmann responded to the onslaught by sending on attacker Uth - a move that was justified by the substitute's clinical finish from just inside the box moments later.
But Liverpool retaliated by crafting another big chance before the break, Firmino seeing a close-range effort from Salah's low cross saved well.
The second half…
The hosts' significant cushion set the tone for the start of the second period, with Klopp's men happy to sit deep and hit on the break.
And, as is so often the case, when the Reds did get the chance to spring, they did so at frightening pace.
One such counter ended in Wijnaldum blasting over after a one-two with Salah, while Mane saw a left-foot strike well parried in similar circumstances shortly after.
The Reds got it right eventually, though, with Henderson capitalising on a loose backpass to pinch the ball and teeing up Firmino for a pass into the net.
Hoffenheim refused to go down without a fight, and grabbed a consolation when Wagner rose highest to head in a deep cross in front of the visiting fans at the Anfield Road end.
But that could not take the shine off a comfortable victory for the Reds that put them back among Europe's elite.
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