Liverpool sealed their Champions League deal by qualifying for the group stage of European football's top competition.
Leading 2-1 from the first leg, the reds rendered the tie over with 3 goals inside the first 22 minutes, with Emre Can on the scoresheet twice and Mohammed Salah scoring his first Anfield goal.
Jurgen Klopp had picked the same side that did the job in the first leg and they were dominated for large periods of this game - coming 989 days since the last Champions League game at Anfield. This team do not look like they will force us to endure such a long wait again.
With Coutinho still sitting on his hands, the reds may have been left wondering who's side in the team he will take should he return, Salah, Mane and Firmino were all excellent throughout the game and Firmino added a 4th either side of two disappointing conceded goals.
Team: Mignolet, Alexander-Arnold, Matip, Lovren, Moreno, Can, Henderson, Wijnaldum, Mane, Salah, Firmino
Bench: Karius, Klavan, Gomez, Milner, Robertson, Solanke, Sturridge
Liverpool set out their stall straight from kick off in an electric Anfield atmosphere. Within 2 minutes the reds had a dangerous free kick after Moreno was fouled just outside the box. Emre Can collected the ball and handed it straight to Trent Alexander-Arnold, the 18 year old who scored the opener in Germany last week.
His free kick rebounded off the wall and Mohammed Salah reacted quickest to get to the header but it went over the bar.
Seconds later Mane found himself one on one with the keeper but the goalie managed to smother the toe-poke.
In the 11th minute, the opener. Firmino finding Mane, and then the backheel to Emre Can who puts the ball in the net, with the slight help of a deflection.
7 minutes later - it's 2-0. Firmino again - finds Wijnaldum who sees his shot rebound off the post and Salah is there, as usual, poised and ready to pounce for the goal.
2 minutes later - the third. Mane and Firmino make the break, Firmino flicks the ball over the penalty area - Salah drags two defenders away and leaves Emre Can all on his lonesome to smash in to the net in the Anfield Road end.
Hoffenheim made a substitution and from the bench Mark Uth grabbed a goal back. Poor defensively by the reds with Dejan Lovren passing a short pass straight back to Wagner who passed out wide for Uth to make it 3-1.
The reds were slightly less dominant in the second half, but they made it 4-1 just after the hour mark.
Jordan Henderson stepping up to put pressure on Kevin Vogt after he collected a poor pass, and nipped the ball away from him. He found Firmino who deservedly added a goal to his night's excellent work.
But there was still time for another away goal, highlighting the reds major frailty - defending.
Kramaric chips the ball across and Wagner heads past a statue-esque Liverpool defence and goalkeeper.
4-2.
But there was never going to be any doubt after the reds blistering opening and Liverpool comfortably qualify for the Champions League group stage.
It was the 20th time that Anfield has saw the reds score 4 or more goals in the European Cup, and the first time since that marvellous March evening when Real Madrid were convincingly beaten 4-0.
The draw for the group stage will be held tomorrow night at 5pm UK time.