The Chilean opened the scoring by firing home a rebound before Muller made the result safe after enduring a barren Euro 2016 campaign for his country.
The Chilean opened the scoring by firing home a rebound before Muller made the result safe after enduring a barren Euro 2016 campaign for his country.
The German Cup final went to penalties for the first time since 1999, with the Brazilian scoring Die Roten's fifth penalty to hand Pep Guardiola's men the trophy.
Xabi Alonso's corner was met by the Germany international's head to hand Die Roten the lead and his penalty later confirmed victory, as they ended the visitors' cup aspirations.
The Bundesliga title contenders kept up the pace at the top of the table with a routine win at Signal Iduna Park on Sunday.
The Poland international's first-half double proved decisive as Pep Guardiola's charges won their fourth straight Bundesliga crown at the Audi Sportpark on Saturday.
The Austria international struck early in the second half to secure three points for the Bavarians, who have gone eight points clear ahead of Dortmund.
The German champions had picked up just one point from their last two games, but had no trouble in a dominant display ahead of their Champions League tie with Juventus.
A win for Borussia Dortmund against Stuttgart means Pep Guardiola's men must wait for the title celebrations to begin but they did their part with a win in Berlin.
The Pole struck as nine minutes to give three points to the champions, who avoided a Champions League hangover to move further clear at the top.
A fiercely tactical battle at Signal Iduna Park could not produce a decisive breakthrough as Thomas Tuchel's men missed the chance to close the gap to two points.