Pep Guardiola’s side will face Borussia Monchengladbach in Sunday’s final, who beat Borussia Dortmund 1-0 in the other semi-final.
Bayern’s early pressure paid dividends in the 12th of the 30 minute half when Boateng toe-poked home after Jaroslav Drobny had denied Claudio Pizarro twice in succession.
Hamburg looked to level as the game moved towards half-time but Tom Starke was alert to deny Jacques Zoua.
Maximilian Beister should have restored parity just after the interval but, through on goal, he steered his effort wide.
The defending Bundesliga, DFB Pokal and Champions League winners punished that miss minutes later when Mandzukic latched on to a Xherdan Shaqiri lay-off to fire home 11 minutes into the second half.
Kroos then added to the Bavarians lead with a shot from distance with 44 minutes on the clock before Meuller headed home Philipp Lahm’s cross to put added gloss on an already polished performance in the 52nd minute.
Although not on the scoresheet, Thiago Alcantara slotted into midfield effortlessly alongside Kroos in a performance that re-affirmed the Bavarians’ ominous strength in depth - and laid down a marker for the season to come.