Emre Can fired Liverpool in front in the 10th minute after a slick move from Sadio Mane.
Mo Salah tapped in the second soon after and seemed surprised that the flag stayed down, but there was nothing controversial about Can’s second, started again by Mane.
Mark Uth pegged one back but the Germans still have a mountain to climb with Liverpool 5-2 up on aggregate.
Victory tonight secures a return to the Champions League group stage for the Reds.
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Liverpool XI: Mignolet, Alexander-Arnold, Matip, Lovren, Moreno, Henderson, Can, Wijnaldum, Mane, Salah, Firmino
Hoffenheim XI: Baumann, Nordtveit, Vogt, Hübner, Kaderabek, Zuber, Geiger, Gnabry, Demirbay, Kramaric, Wagner
Thousands of fans made the long trip from Germany for the match.
Almost 3,000 were seen marching to Anfield from the city’s Williamson Square.
And they left major traffic disruption and chaos in the city centre as they headed towards the famous ground.