Pep Guardiola was impressed with the constant attacking on show by the Bavarians to secure a 4-1 cup win and reach the third round, while Schalke avoided an upset against Darmstadt
Thomas Muller struck twice at the Allianz Arena on Wednesday, with Claudio Pizarro and Franck Ribery also getting on the scoresheet as Bayern never looked in trouble against their opponents.
Bayern made a quick start and goals within five minutes from Muller and Pizarro put the hosts 2-0 up with 22 minutes on the clock.
Didier Ya Konan halved the deficit before the break but a relentless Bayern secured the win, their ninth in 11 competitive games under Guardiola, in the second half.
The Spaniard was proud of their victory over tough opponents in the second round of the competition, praising his players' mental strength as key to the triumph.
"We played very well, but in the last 10-to-15 minutes of the first half we lost our shape," he told the club's official website.
"I'm surprised at the way we played in the second half. It's our mentality, we just kept attacking. We've won a tough game against a great team. I'm surprised by Hannover's performance.
"It's not possible to win trophies with only 11 players. We have lots of good players and all of them are good enough to start."
Schalke avoided a cup upset as they eventually broke down Darmstadt to win 3-1.
The top-flight team took the lead in the 35th minute as Jefferson Farfan converted a penalty, however their lead lasted a minute as Hanno Behrens equalised.
Darmstadt kept themselves in the game until the 58th minute when Benedikt Howedes put Schalke back in front and Max Meyer secured their progression with a goal in the closing minutes.
Last year's beaten finalists Stuttgart crashed out to Freiburg as Matthias Ginter and Mike Hanke secured a 2-1 win for Christian Streich's side.
Kaiserslautern produced the surprise of the night as they knocked out Hertha Berlin 3-1. The second division side had to come from behind after Peter Niemeyer opened the scoring for Hertha in the 25th minute.
Second-half goals from Mohammadou Idrissou, Karim Matmour and Olivier Occean booked Kaiserslautern's place in the next round.