Both sides drew 1-1 at Signal Iduna Park last night.
But within three minutes of the restart, defender Mats Hummels headed home the equaliser in what proved to be the last goal of an entertaining contest.
Hummels developed into one of the world's finest centre-halves under Klopp, and speculation mounted last month that the 48-year-old coach would try take him to Anfield this summer (The Star).
Regardless of whether that is true, the duo clearly have plenty of affection for one another as the pair exchanged a warm hug after the final whistle in Germany.
Having spent seven years as Dortmund boss, winning two Bundesliga titles and guiding them to a Champions League final in 2013, Klopp's return was a huge subplot in this.
But Klopp indeed made it clear where his loyalties now lie after passionately celebrating Origi's opener with the same enthusiasm Dortmund fans had revelled at for so long.
Both sides do it all again at Anfield next Thursday.