Klopp, the former Liverpool, Borussia Dortmund and Mainz coach, took over his new duties as Red Bull's head of global soccer on January 1 and took the first opportunity on Sunday to see the energy drinks manufacturer's German representatives Leipzig in competitive action.
Klopp can have had few complaints as he watched the 21-year-old Xavi Simons open the scoring and then cancel Mitchell Weiser's response, before Benjamin Sesko, also 21, made it 3-1 with a brilliant strike from distance after the break.
Both Xavi and Sesko fit the profile of highly talented young players that Klopp will be expected to develop and attract to the growing Red Bull stable of clubs.
Leipzig substitute Christoph Baumgartner scored in the final minute before Bremen's Oliver Burke scored in stoppage time.
Klopp had also been in Paris on Saturday to see second-tier Paris FC beat Amiens 1-0.Â
Among his tasks there is turning the club into one of France's best under the ownership of the country's richest family, the Arnaults of luxury empire LVMH. The family's takeover of the second-tier club includes bringing Red Bull on board as a minority stakeholder.
Leipzig have struggled so far this season, losing all their games in the Champions League and dropping points in seven of their 16 games in the Bundesliga.
But the win sent them back up to fourth, two points above Mainz, who had beaten bottom side Bochum 2-0 on Saturday.
In Sunday's late game, last term's runners-up VfB Stuttgart moved up to seventh with a 1-0 win at Augsburg thanks to a goal from the returning Deniz Undav.
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