Two goals from Claudio Pizarro and two from Mario Gomez helped Bayern seal a season-record 26th Bundesliga win in a one-sided encounter that moved them on to a record-equalling 81 points with four games remaining.
Borussia Dortmund, who have their own Champions League last-four clash against nine-times European champions Real Madrid on Wednesday, secured their spot in the competition next season with a 2-0 win over Mainz 05.
Bayern, who are chasing a treble having also advanced to the German Cup final in midweek, looked to have lost none of their edge despite clinching the league title two weeks ago.
"The players showed that there is no B team but just one A team," said coach Jupp Heynckes, who rested several key players ahead of Tuesday's game against Barcelona.
"My players just have fun playing football and they were all fully motivated. We put down the foundations for a big win in the first half."
LUCKY LEAD
The visitors grabbed a lucky lead when David Alaba raced into the box and his cutback for Gomez was turned in by Hannover defender Lars Stindl, who was trying to clear.
There was nothing lucky about their second goal, however, as the evergreen Pizarro played a superb pass for Franck Ribery, who notched his eighth goal of the season in the 23rd minute.
The 34-year-old Peruvian, the third-choice striker this season behind Mario Mandzukic and Gomez, then put another immaculate pass through for Gomez who had no trouble scoring from close range to give them a 3-0 halftime lead.
The Germany forward, who could be leaving Munich at the end of the season, added his second goal in the 62nd, tapping in an Alaba cross.
Alaba then played in Pizarro for his first goal of the day with 19 minutes remaining. He added another in the 86th after Hannover had scored a consolation goal.
"We all wanted to prepare well for Barcelona," Bayern keeper Manuel Neuer said. "We succeeded in doing just that. We played very well and had an outstanding first half."
Dortmund scored at the start and the end of their match against Mainz through Marco Reus and Robert Lewandowski to stay second on 61 points, 20 behind Bayern, but eight ahead of Bayer Leverkusen, who are third on 53 after crushing 10-man Hoffenheim 5-0.
Dortmund are now assured of an automatic Champions League spot after their fourth-placed Ruhr valley rivals Schalke 04 lost 1-0 at Eintracht Frankfurt. Schalke are on 46 points and cannot catch Dortmund.
Two goals from new Hamburg SV captain Rafael van der Vaart gave them a 2-1 win over Fortuna Dusseldorf.
The win puts them in eighth place on 44 points.
It was a different story for fellow northern club Werder Bremen, who slumped to a 3-0 home defeat by VfL Wolfsburg and have now failed to win in their last nine games.
Teenager Maximilian Arnold put Wolfsburg
