Pep Guardiola’s side did not let up after the interval, as Mario Mandzukic, Tomi Kroos and Thomas Muller all added to the scoreline to cap off a dominant performance from the defending Bundesliga, DFB Pokal and Champions League winners.
Bayern will now face Borussia Monchengladbach in the final on Sunday, after the tournament hosts dispatched Borussia Dortmund 1-0 with a last-gasp penalty in Saturday’s earlier semi-final.
Pep Guardiola shuffled his squad, with Tom Starke and Claudio Pizarro handed starts, but all eyes were on big-money acquisition Thiago Alcantara, who began in midfield alongside Kroos, who missed the second half of the 2012-13 season with injury.
It was a typically strong beginning to the game for Bayern, who kept most of the action concentrated around the Hamburg penalty area during the initial stages.
Mandzukic came within inches of heading them into an 11th minute lead, but Jaroslav Drobny managed to get fingertips on the attempt, pushing it onto the far post.
The respite would last all of one minute, however, as the Bavarians took the lead on their next attack. Drobny was again outstanding to deny Pizarro twice in quick succession from close range, but was helpless when Boateng poked home at the third time of asking.
There were a few signs of life from Hamburg towards the end of the first half, and Starke was forced to use his feet to deny Jacques Zoua at the post, one of a series of testing deliveries into the area from Thorsten Fink’s team.
And moments into the second period, Maximilian Beister nearly brought Hamburg back on terms when he was put through on goal, but he could not steer his finish on target.
Bayern would make them pay for four minutes later though, when Xherdan Shaqiri cushioned a high ball into the path of Mandzukic, who stabbed home clinically from inside the area.
It was 3-0 within moments, courtesy of Kroos, who powered home from the edge of the area, though Drobny looked disappointed with letting the shot slip past him.
There was only one side remaining in the game at that point, and Bayern duly added a fourth with eight minutes to go, Muller heading home with authority after a flighted ball by Philipp Lahm from the flank.
And with two minutes remaining, Arjen Robben came within inches of making it five with a trademark move, cutting in from the right onto his left foot, but his low shot whistled past the post.