Needing 310 to make the home team bat again, Bangladesh were bowled out for 178 in their second innings half an hour after lunch on the third day.
Waugh, who scored an unbeaten century in Australia's total of 407 for seven to become only the second player to make hundreds against every Test-playing nation, claimed his 37th win as skipper, eclipsing the record of 36 set by West Indian Clive Lloyd.
It is doubtful whether Waugh, named man of the match, has had many easier victories in his 50 matches in charge of Australia, but the 38-year-old said Bangladesh were not as easy as everyone expected.
"It went pretty much according to plan. Bangladesh batted better in the second innings but we always expected to win," Waugh said.
"We wanted to get them in early and try and knock them over early and put some pressure on them but I thought they showed some real character."
COMPETING HARD
Bangladesh, yet to win a match after being elevated to Test status three years ago, failed to offer any serious challenge to the world's top-ranked team in what proved to be a mismatch.
They were skittled out for 97 in the first innings but showed some hint of resistance second time round with Habibul Bashar, the only Bangladesh player to reach 1,000 Test runs, top-scoring with 54.
Al Sahariar made 36 and Hannan Sarkar 35 but only one other player reached double figures as leg spinner Stuart MacGill ripped through the batting order with five wickets.
"There's a couple of positives but really there's a fair bit of distance between the two teams," Bangladesh coach Dav Whatmore said.
"I don't want to jump to any conclusions given the class of opposition that we've faced...but I think the team is really competing hard and that's a nice little springboard going into the next game.
MacGill captured the vital wicket of Bashar when he bowled him with a googly, triggering a collapse that brought the match to an abrupt end.
"I guess I've learnt through my career that when you get a chance to get the ball in your hand you've got to make the most of it no matter who the opposition is," MacGill said.
The second test in Cairns starts next week.
