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 its perfect start to the season with a convincing 3-1 victory over Mainz at the Allianz Arena.
Mario Mandzukic and Bastian Schweinsteiger gave the host 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 Nurnberg 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 Nurnberg 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 its unbeaten start to the season with a 2-0 victory at Greuther Furth, which 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 its first point of the season in a lacklustre goalless draw against newly-promoted Fortuna Dusseldorf, which is the only team in the Bundesliga not to have conceded a goal yet.