Bayern Munich maintained their perfect start to the season with a convincing 3-1 victory over Mainz.Bayern Munich maintained their perfect start to the season with a convincing 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 they were made to sweat when 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 Bundesliga. The 71,000 fans inside the Allianz Arena had barely had enough time to locate their seats before Mandzukic fired Bayern in front. Thomas Muller, the league's top goalscorer before the weekend, unselfishly turned provider for Mandzukic to join him on three goals for the season with a simple tap-in from close range. Mandzukic almost moved clear at the top of the scoring charts just three minutes later, but Christian Wetklo was this time on his line to deny him. Bayern were finding it all too easy to get in around the back of the Mainz defence and a cross from Holger Badstuber set up Schweinsteiger to make it two with a close-range header in the 13th minute. After winning their first two games by comfortable margins, Bayern were well on course for yet another parade victory. But perhaps with their first Champions League tie of the season against Valencia this coming Wednesday on their minds, they started to sit on their lead from as early as the 20th minute. Mainz were unable to take advantage, though, and as they showed no sign of finding a way back into the game, coach Thomas Tuchel hauled two players off before the interval. Marco Caligiuri and Marcel Risse were replaced by Elkin Soto and Szalai in the 37th minute. The latter gave Mainz hope from the penalty spot in the 59th minute after Dante went in dangerously on Julian Baumgartlinger inside the area, giving away a penalty. Bayern had to take the game more seriously again and Mandzukic went close to restoring their two-goal lead when he hit the post before hitting the rebound over. Mainz were in a more attacking mood too and this made the game open up with Kroos given room to volley in Bayern's third in stoppage time with Javi Martinez the provider from the right.