The Reds entered the match as the favourites to advance after recording a 2-1 victory in the first leg last week, and four more goals in the return fixture saw the five-time European champions triumph 6-3 on aggregate.
Liverpool boss Jurgen Klopp named an unchanged team from the first leg last week, which meant recalls for Mohamed Salah, Dejan Lovren, Trent Alexander-Arnold, Alberto Moreno and Emre Can following Saturday's win over Crystal Palace.
The home side had a half-chance to take the lead inside the opening three minutes when a deflected free kick from Alexander-Arnold landed at the head of Salah, but the summer signing from Roma could only head over the crossbar.
Hoffenheim were very much a part of the argument in the early stages, however, and Gnabry had a clear opportunity inside the Liverpool box in the seventh minute, but the offside flag was raised after Liverpool's defence held their line.
A goal was always coming after such a bright start to the match, and Liverpool made the breakthrough in the 10th minute when Can collected a pass from Mane before sliding the ball into the back of the net courtesy of a deflection.
Eight minutes later, Liverpool scored their second of the match when Salah had the simple task of placing the ball into the back of the net after Georginio Wijnaldum had hit the post with an effort from just inside the Hoffenheim box.
Liverpool were purring, and the Reds made it 3-0 in the 21st minute when Can grabbed his second of the night at the far post after Roberto Firmino had lifted a pass into the path of the German international.
Hoffenheim made their first change of the night in the 24th minute as Mark Uth replaced former West Ham United midfielder Havard Nordtveit, which saw the Bundesliga side change formation as they looked to somehow find a route back into the tie.
Gnabry should have made it 3-1 in the 25th minute after breaking into the Liverpool box, but the former Arsenal youngster chipped wide of the far post.
Hoffenheim were on the scoresheet three minutes later, however, when substitute Uth found the bottom corner with a well-placed finish after Wagner had released his teammate in a dangerous position.
Liverpool should have scored their fourth of the night in the 37th minute when Salah's low cross found Firmino inside the Hoffenheim box, but Baumann was on hand to make another smart save, before Can curled a low effort just wide of the German outfit's post four minutes before the break.
Wijnaldum had a brilliant chance to score a fourth for Liverpool in the 55th minute after a smart pass from Salah had released the Dutchman inside the box, but Baumann made another super save, before the Hoffenheim goalkeeper kept out a powerful effort from Mane two minutes later.
Baumann was then again called into action just before the hour to keep out a low strike from Wijnaldum, who had met a cross from the impressive Alexander-Arnold.
Liverpool found their fourth of the evening in the 63rd minute, however, when Jordan Henderson raced into the Hoffenheim box before squaring the ball to Firmino, who could not pass up the chance to make it 6-2 on aggregate.
Adam Szalai had a half-chance for the visitors 15 minutes from time after a smart cross from Wagner, but Joel Matip just did enough to make the clearance as Liverpool eased their way to the group stage of the competition.
Hoffenheim did score a second in the 79th minute when Wagner headed a Kramaric cross into the back of the net, but it was a case of too little, too late as Liverpool ensured that they would be present in tomorrow afternoon's group-stage draw, which takes place in Monaco.