Ponting finished unbeaten on 118, nursing the tailenders on the final day to steer Australia to their victory target of 307 and deny Bangladesh only their second victory in 43 Tests.
Ponting received solid support from fast bowlers Brett Lee [ Images ] (29) and Jason Gillespie (seven not out) after wicketkeeper Adam Gilchrist [ Images ], who scored a century in the first innings, and Shane Warne [ Images ] had fallen early to give Bangladesh a scent of victory.
Bangladesh, who scored 427 in their first innings before bowling Australia out for 269 to take charge of the match, lost their two previous tests against Australia in 2003 by an innings. They had won only one of their previous 42 Tests since 2000, that victory coming over a depleted Zimbabwe side.
The second and final Test starts in Chittagong on Sunday.