Borussia Dortmund's dismal domestic season continued as they were beaten at home for the third time, going down 1-0 to Hannover.
Hiroshi Kiyotake scored the only goal of the game midway through the second half as the mid-table Reds increased their advantage over Dortmund to six points, despite ending the game with only 10 men as Ceyhun Gulselam saw red.
The Westphalians, who have picked up three wins out of three in the Champions League this season, find themselves just one point and one position above the relegation zone with only seven points from nine Bundesliga fixtures.
Ciro Immobile was sent on by Klopp to vary things in attack, but for all their efforts, they could not find a way back into the game as they crashed to a fifth league defeat in their last six games.
Christian Gentner scored an 84th-minute winner as Stuttgart won an extraordinary game against Eintracht Frankfurt 5-4 at the Waldstadion.
Alexander Madlung put Frankfurt in front before two goals from Martin Harnik gave Stuttgart the lead at half-time.
Gentner extended their advantage to 3-1 early in the second half, but Alexander Meier, Stefan Aigner and Madlung again struck in the space of eight manic minutes to put Frankfurt back in front.
There were more twists to come, though, with Timo Werner levelling things up again at 4-4 before Gentner netted his second to earn Armin Veh victory over his former club, who ended an incident-packed game with 10 men as Haris Seferovic saw red late on.
Hoffenheim extended their unbeaten start to the season and moved up to second in the table thanks to a 1-0 win over Paderborn.
Kevin Volland scored the only goal of the game after Sebastian Rudy had missed an early penalty for Markus Gisdol's men.
The win -- Hoffenheim's fourth of the season -- took them to within three points of leaders Bayern Munich, who face the side Hoffenheim replaced in second, Borussia Monchengladbach, on Sunday.
Roberto Di Matteo lost his first game since taking charge of Schalke as Bayer Leverkusen took the honours with a 1-0 win at the BayArena.
Hakan Calhanoglu netted the only goal of the game with a trademark free-kick which beat Ralf Fahrmann to lift the Werkself up to fourth in the Bundesliga.
After beating Hertha Berlin and Sporting Lisbon in his first two games in charge, Di Matteo failed to make it three out of three with defeat on his first trip away from the Arena AufSchalke to leave Schalke in 12th.
Hamburg's recent mini resurgence was brought to an abrupt end they crashed to a 3-0 defeat to Hertha Berlin at the OIympiastadion.
A second-half brace from former Hamburg midfielder Anis Ben-Hatira, either side of a John Heitinga goal, earned Jos Luhukay's men the win as the Old Lady put some daylight between themselves and the bottom three.
Hamburg, in contrast, missed the chance to move out of the relegation zone in view of Borussia Dortmund's defeat to Hannover, suffering instead a setback which will also dent morale when it seemed they had turned the corner.
Augsburg lifted themselves into mid-table with a 2-0 triumph over winless Freiburg at the Augsburg Arena.
Paul Verhaegh put the hosts in front from the penalty spot after 11 minutes and Halil Altintop sealed the points midway through the second half.
The result left the visitors second from bottom in the standings.