A stunning free-kick from Trent Alexander-Arnold in the first half put Jürgen Klopp's men in front at Rhein-Neckar-Arena, and the advantage was later doubled via James Milner's deflected effort.
Mark Uth grabbed a goal back for the Bundesliga side with three minutes left on the clock but the Reds have taken control of the tie.
See the story of the game in photographs below.
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