Dortmund, Germany, 18 August 2021 (dpa/MIA) - Goals from Robert Lewandowski and Thomas Mueller gave Bayern Munich a deserved 3-1 Super Cup triumph away to Borussia Dortmund on Tuesday and acted as a timely reminder the champions will not give up their Bundesliga title without a fight. Bayern were held to a draw at Borussia Moenchengladbach in last weekend's league opener as a bumpy start under new coach Julian Nagelsmann continued while Dortmund - under their own new boss Marco Rose - thrashed Eintracht Frankfurt. But an improved display from Bayern, tightening at the back to largely keep Erling Haaland quiet while being a constant threat in attack, earned a deserved first win at the club for Nagelsmann and also brought his maiden title as coach. Lewandowski's thumping 41st minute header broke the deadlock and Mueller, with a tap-in straight after the re-start doubled the lead. Dortmund replied through a brilliant goal from Marco Reus midway through the second half but a hideous error from Manuel Akanji let Lewandowski complete his brace and seal matters. "We defended well, especially in the first half," Nagelsmann told broadcaster Sat1. He praised the "aggression" of his team in winning the ball back and though pleased to have the trophy, stressed "we have another game soon," when asked about potential celebrations. Both sides and the 25,000 fans attending under coronavirus rules observed a minute's silence for Bayern legend Gerd Mueller, who died aged 75 on Sunday, and the players wore black armbands. Bayern made the quicker start to immediately expose full back Felix Passlack, whose giveaway led to Kingsley Coman shooting over. Reus had a shot saved but in the first half Haaland was hardly a factor other than setting up Youssoufa Moukoko to score when well offside. "We had our chances," Reus told Sky. "That's why we're disappointed. Everything wasn't perfect but the willingness and energy was there." Dortmund had a massive let-off when Mueller and Lewandowski were blocked from Joshua Kimmich's quick free-kick but fell behind shortly before the break. Passlack bore the brunt as a hopeful ball to Haaland was returned down his flank with interest. Serge Gnabry's quick feet made space and his cross was met by the unstoppable Lewandowski. And in the 49th minute it was full back Alphonso Davies who took advantage down Passlack's wing to cross and though Lewandowski miscued his flick, Mueller was left with an open goal. "It means a lot, it's the next title," Lewandowski said. "We can play better. But we're at the start of the season, we need more time." Lewandowski did score his second second, in the 74th, when returning substitute Corentin Tolisso blocked Akanji's pass into his path and he finished coolly. "I would like to have won my first trophy here but we can take away a lot of positives despite the result," said Dortmund keeper Gregor Kobel, who was blameless for the goals. "We are a great group on a great path." With nothing to lose Dortmund had been pushing forward and 10 minutes earlier were rewarded through Reus' shot curled into the top corner from outside the box. It came after Haaland had a goal rightly disallowed for a marginal offside but with Dortmund's momentum halted Bayern lifted the trophy for the sixth time in the last decade. Whether it is a signal of what is to come in their bid for a record-extending 10th Bundesliga title remains to be seen.