Healy hit a glorious unbeaten 113, coming just four days after her equally brilliant 142 that saw off hosts India at the same Visakhapatnam stadium, this time sharing a magnificent unbroken double-century opening partnership with Phoebe Litchfield (84no) to race to their target of 199 in just 24.5 overs.
Ironically, the supreme professionalism of Thursday's chase as the pair put on 202 came after perhaps Australia's shoddiest display in the field under Healy's stewardship, with the skipper scolding herself in particular for spilling two of the six catches that went down.
"I thought I was a little bit poor behind the stumps, and probably a little bit as skipper as well tonight, but we'll take the two points and move on," she shrugged.
"I was a little bit disappointed with my glovework and I had a little bit to make up for with the bat, and luckily got the job done."
Since data was first taken on fielding statistics in 2013, the half-dozen dropped catches represented Australia's worst fielding display at a Women's World Cup, leaving Healy to shrug: "Maybe it's just that time of the tournament - we've been here a little while, and it's something we'll reflect on."
It helped Bangladesh eke out 9-198 after they'd chosen to bat, their highest total in an ODI against Australia, with Sobhana Mostary compiling the first half-century ever for the Asian side against the world champs.
But Alana King's mesmeric unbroken 10-over spell, in which she took 2-18 with four maidens, was key to ensuring Australia's target wasn't too challenging.
Healy was delighted to learn that the victory, which puts her unbeaten side top of the group table on nine points after four wins and a wash-out, guarantees them a place in the last-four. "That's really cool," she said at the presentation.
The 35-year-old skipper sped to her hundred off just 73 balls, the fastest century of the tournament, and ended with 20 boundaries as she pulled away from Litchfield later in the innings after they'd gone practically boundary-for-boundary towards their fifties.
Left-hander Litchfield struck 12 fours and a six, getting to her first World Cup half-century off 46 balls soon after Healy got there off 43. They went on to record the third-highest partnership by any Australian pair at a Women's World Cup.
Earlier, during the uncharacteristically poor fielding display, Healy spilled the simplest of edges off Darcie Brown and also failed to grasp a difficult lofted one off Annabel Sutherland. Frustratingly, she also did take a clean catch off Brown but didn't have it reviewed when the umpire rejected her appeal.
The recalled Brown sent down the fastest deliveries at the World Cup so far but still ended up with the expensive figures of 0-52 off her nine overs.
Instead, it was the spinners who thrived, led by King, whose spell could have been even productive if Beth Mooney hadn't dropped one in the slips.
Fellow spinners Georgia Wareham (2-22 off seven) and Ash Gardner (2-48 off nine) both chipped in, while Sutherland consolidated her position as the tournament's leading wicket-taker with her 2-41, taking her tally to 13.
Rubya Haider's 44 and Mostary's unbeaten 66 off 80 balls took Bangladesh to their record total against the Aussies, but the total was made to look easy meat by a side who had chased down 330 against India four days earlier.
"It's always nice when you've got the 'Q' next to your name in a World Cup," said player-of-the-match King. "No doubt it doesn't stop here. We look forward to going back to Indore to take on England and South Africa."
