Bayern Munich enjoyed a convincing win away to Kaiserslautern as Freiburg and Cologne recorded their first Bundesliga wins of the season.
Promoted Augsburg await their first victory of the campaign after losing at Nurnberg, while Werder Bremen left it late to beat Hoffenheim.
Mario Gomez helped himself to a hat-trick as Bayern won 3-0 away to Kaiserslautern, who finished the game with 10 men.
Germany international Gomez opened the scoring from the penalty spot on 37 minutes following Rodnei's handball and made it 2-0 on 55 minutes after seeing another spot-kick saved.
Gomez completed his hat-trick on 69 minutes before Kaiserslautern's Ivo Ilicevic was sent off in the final minute.
Cologne climbed off the bottom of the table as two substitutes worked the oracle in a thrilling 4-3 victory away to Hamburg.
Hamburg took the lead through Mladen Petric's 11th minute penalty, but Cologne levelled through Adil Chihi and then went ahead on 49 minutes thanks to Milivoje Novakovic.
New signing Slobodan Rajkovic marked his Hamburg debut with an equaliser on the hour mark and Son Heung-min's goal two minutes later appeared set to give the hosts the points.
However, substitute Christian Clemens drew Cologne level again with three minutes to go and fellow sub Kevin McKenna pounced for the winner just 60 seconds later.
Freiburg produced a commanding performance on home soil to gain a first win after a 3-0 success over Wolfsburg.
Oliver Barth and Erik Jendrisek scored before half-time and Cedric Makiadi put the seal on the win with the third goal just before the hour.
Substitute Markus Rosenberg was the hero as his 83rd minute effort enabled Werder Bremen to come from behind to win 2-1 at Hoffenheim.
Earlier, Hoffenheim had taken the lead through Roberto Firmino only for Bremen to level within a minute through Marko Arnautovic.
Nurnberg edged out Augsburg 1-0 at home thanks to substitute Alexander Esswein's 76th minute goal.
Later on in the evening, Borussia Dortmund moved up to fourth after they earned a point following their goalless draw against Bayer Leverkusen.
Michal Kadlec was dismissed for a bad tackle after 64 minutes which left Leverkusen with just 10 men for the remainder of the game.
But Dortmund failed to press home their numerical advantage as Mario Gotze was given his marching orders after 77 minutes for a professional foul.