Leverkusen are up to third in the Bundesliga, but trail champions Bayern by a massive 24 points and the gulf in the league table showed up clearly in this semi-final.
"We were very effective and the team worked really well together," beamed Muller after Bayern's masterclass in attacking football. "We really deserved it, the team performance was great. Of course we want more (titles), we can feel that something is possible this season.”
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Muller, the man of the match, scored and hat-trick and helped set up the visitors' first goal for Javi Martinez after only three minutes. Robert Lewandowski added a second after just nine minutes at the BayArena in Leverkusen.
Bayer captain Lars Bender gave the hosts hope with a 16th-minute header while the Bayern defence appealed for an offside call which never came.
Bayern stormed away in the second half as their star-studded attack turned on the style. Muller netted his first on 52 minutes after good work from Thiago Alcantara, who hit their third eight minutes later.
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The Spain international ran across goal and pulled back a sublime shot which wrong-footed Leverkusen goalkeeper Bernd Leno. Arjen Robben made it 5-1 when he fired home unmarked in the area on 64 minutes.
Jamaica winger Leon Bailey, a second-half replacement, pulled a goal back for Leverkusen with a stunning free-kick on 72 minutes.
But Mu Muller eller extinguished any hopes of a fight-back with his second and Bayern's sixth as the attacking midfielder scored a classic striker's goal.
When a Thiago pass played him into the area, Muller shielded the ball with his body, then spun around his marker to bang his shot past Leno on 78 minutes.
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