Mats Hummels put Jurgen Klopp's men in front in the 29th minute before Jakub Blaszczykowski added a second 10 minutes later. Robert Lewandowski wrapped up victory in a one-sided encounter in the 78th minute.
Bayern Munich maintained their perfect start to the season with a convincing 3-1 victory over Mainz at the Allianz Arena.
Mario Mandzukic and Bastian Schweinsteiger gave the hosts a two-goal lead within the first 13 minutes, but Adam Szalai reduced the arrears from the penalty spot in the 59th minute.
However, Toni Kroos wrapped up victory with practically the last touch of the game as Bayern made it three wins out of three in the league.
Hiroshi Kiyotake scored one and set up two more as Nuremberg shrugged off a Borussia Monchengladbach fightback to win 3-2.
The Japan international sent in the free-kick from which Timm Klose scored in the 17th minute and then a corner for Timmy Simons to head in after 25 minutes as Nuremberg took a 2-0 lead.
Luuk de Jong halved the deficit in the 45th minute and Granit Xhaka equalised after 53 minutes, but Kiyotake struck the winner in the 55th minute.
Szabolcs Huszti scored his second goal of the game and was sent off for over-celebrating two minutes into stoppage-time as 10-man Hannover clinched a thrilling 3-2 victory at home over Werder Bremen.
Huszti scored the opener in the sixth minute and teed up Leon Andreasen's goal that gave Hannover a 2-0 lead after 10 minutes.
Aaron Hunt converted from the spot to cut the deficit to 2-1 in the 26th minute, and Kevin De Bruyne equalised in the 74th minute.
But Huszti provided the game-winner with time running out. The Hungarian was shown two yellow cards, one for taking off his shirt and then another for jumping up to celebrate with the Hannover fans.
Schalke extended their unbeaten start to the season with a 2-0 victory at Greuther Furth, who lost for the second time in a row at home.
Julian Draxler put the Royal Blues in front early in the second half with a stunning effort from distance and Lewis Holtby added the second in the dying stages of the match.
Stuttgart picked up their first point of the season in a lacklustre goalless draw against newly promoted Fortuna Dusseldorf, who are the only team in the Bundesliga not to have conceded a goal yet.
On Sunday, Eintracht Frankfurt made it three wins out of three and spoiled Rafael van der Vaart's second Hamburg debut as the newcomers won 3-2.
Armin Veh's men signalled their intentions with two goals inside five first-half minutes from Takashi Inui and Olivier Occean.
Hamburg pulled a goal back on the stroke of half time through Heiko Westermann, but they also lost Petr Jiracek to a red card before the interval.
Aigner gave Frankfurt a two-goal cushion to sit on in the 52nd minute, but Heung Min Son made a game of it by scoring a second for Hamburg in the 63rd minute, setting up a tense finale in which Frankfurt held on to join Bayern Munich in a share of top spot.
There was more drama in the day's other game as Freiburg got the better of Hoffenheim 5-3 at the Dreisamstadion with the pressure increasing on the visitors' coach Markus Babbel.
The game started well for Hoffenheim with Matthieu Delpierre putting them ahead in the second minute, but Karim Guede and Max Kruse turned the game around before half-time.
Boris Vukcevic brought Hoffenheim level in the 57th minute before Fallou Diagne headed Freiburg ahead for the second time.
Hoffenheim refused to lie down and they equalised again through Takashi Usami in the 76th minute, but Cedric Makiadi and Sebastian Freis ensured Christian Streich's side were ultimately rewarded with all three points.
On Friday, Augsburg and Wolfsburg both had to settle for a share of the spoils as they played out a 0-0 draw.
Sunday's Bundesliga Results
Saturday's Bundesliga Results
Friday's Bundesliga Results