It was Australia's biggest victory since 2019 and the perfect present for Graham Arnold, who took charge for the 59th time, a record for a Socceroos coach.
Substitute Jamie Maclaren hit a second-half hat-trick in front of nearly 21,000 and it could have been even worse for Bangladesh but Massimo Luongo missed a late penalty.
"Seven goals, but it could have been more, for me too, but three points and we move on," said Melbourne City striker Maclaren.
"I'm not even sure (goalkeeper) Maty (Ryan) had a save to make so proud of the team, but we obviously know the next games are going to be harder."
Australia are in Group I alongside Palestine and Lebanon, who meet in Sharjah.
In Group B, Ayase Ueda also scored a hat-trick as Japan got their bid to reach an eighth straight World Cup off to an emphatic start with a 5-0 win over Myanmar.
Japan coach Hajime Moriyasu demanded even more from his side despite their handsome victory.
- Son hits screamer -
Not to be outdone, Jurgen Klinsmann went a little way towards silencing the doubters in South Korea as his side strolled to a 5-0 thumping of Singapore in Seoul.
Tottenham Hotspur forward Son Heung-min was among the goal-scorers, and it was a cracker, bending the ball left-footed into the top corner from outside the box.
"A huge compliment to the team, a very professional performance," German legend and South Korea coach Klinsmann said.
"Five-nil is a nice scoreline to read but it doesn't really show you the energy and effort you have to invest in order to get to that scoreline," he added.
Also in Group C, Wang Shangyuan scored 16 minutes from time to give China a 2-1 win in Thailand and join South Korea at the top of the early standings.
China host South Korea on Tuesday.
In Group F, Vietnam beat the Philippines 2-0 away.
- Qatar hit eight -
Among games later Thursday, Saudi Arabia comfortably beat Pakistan 4-0 and 2022 World Cup hosts Qatar crushed Afghanistan 8-1 in Doha, with Almoez Ali scoring four of their goals, including two from the penalty spot.
Palestine began their quest for a place at the World Cup with a goalless draw against Lebanon in their Group I World Cup qualifier in Sharjah.
The match was played at Khalid Bin Mohammed Stadium in Sharjah because of a one-match stadium ban on ‘host’ Lebanon following unruly scenes in their qualifier against Syria in Beirut last year.
A record eight direct spots and one intercontinental playoff berth are at stake for 2026 for Asian Football Confederation sides, from nine groups of four.
The top two from each group go through to the final qualifying round in Asia.