Bayern Munich maintained their perfect start to the Bundesliga season on Saturday when a 3-1 home win over Mainz gave them a third win in three matches. Bayern stay top having raced into a 2-0 lead at their Allianz Arena as Croatia striker Mario Mandzukic bagged his fifth goal in four games after just two minutes before midfielder Bastian Schweinsteiger added a second, 11 minutes later, with a header. Mainz pulled a goal back when midfielder Adam Szalai converted a 59th-minute penalty, but Germany midfielder Toni Kroos made sure of the three points for Bayern with a goal in the 92nd minute. Munich won without Franck Ribery and Arjen Robben after they both picked up thigh injuries in the final training session, while new signing Javier Martinez only came off the bench for the final 15 minutes. \"We produced an excellent half hour of football, the goals were outstanding, but we were too passive in the 15 minutes before the break,\" said Bayern coach Jupp Heynckes. \"The 3-1 was well deserved, especially after Javi Martinez came on, we played well going forward and were very intelligent in our play.\" With German Chancellor Angela Merkel watching in the stands, defending champions Borussia Dortmund enjoyed a convincing 3-0 win over Bayer Leverkusen to move up from sixth place to third at a sold-out Signal Iduna Park. The hosts went ahead after Germany defender Mats Hummels headed home on 29 minutes from a corner, then Poland captain Jakub Blaszczykowski made it 2-0 with a crisp strike on 39 minutes. Compatriot Robert Lewandowski added the third on 78 minutes with a header. \"We will take everything positive from this game into the next against Ajax,\" said Dortmund coach Jurgen Klopp ahead of Borussia\'s opening Champions League home match against the Dutch champions on Tuesday. \"For the first time this season, we did everything on the pitch which we had planned to do.\" Hanover are second after a dramatic 3-2 win over Werder Bremen at home in the north German derby with midfielder Szabolcs Huszti scoring the winner in the 92nd minute. It was the Hungarian\'s second of the game and his enthusiastic, shirtless celebrations earned him two yellow cards in quick succession and he finished the match being sent off, seconds before the final whistle. Japan midfielder Hiroshi Kiyotake is making a name for himself in Nuremberg after scoring a 55nd-minute winner in his team\'s 3-2 win at Borussia Moenchengladbach to put his team fourth. Kiyotake set up both of Nuremberg\'s goals for Timm Klose and Timmy Simons as the guests took a 2-0 lead before Gladbach\'s Dutch striker Luuk de Jong and Swiss midfielder Granit Xhaka scored to level. Stuttgart were held to a goalless draw at home to Fortuna Duesseldorf while Schalke 04 have the chance to get back amongst the league leaders when they play at Greuther Fuerth on Saturday night. On Friday, Wolfsburg were held to a goalless draw by Augsburg, while on Sunday Eintracht Frankfurt host Hamburg and Freiburg are home to Hoffenheim.