Ellyse Perry (65no off 64 deliveries) and Annabel Sutherland (74no off 52) added 137 for the third wicket to chase down the Bangladesh total of 172 all out inside 23 overs.Â
Australia lost openers Georgia Voll (11) and Beth Mooney (21) early in the run chase at Allan Border Field..
Mooney, in her 100th ODI match, was cleaned up by the second delivery in ODI cricket by Bangladesh debutant quick Disha Biswas.
From that moment it was plain sailing for the hosts as Perry and Sutherland went through the gears.
Australia captain Tahlia McGrath said the duo were "unbelievable cricketers" who kept improving their games
Earlier Schutt, player of the match and of the series, continued her love affair with Allan Border Field with another masterclass.
Schutt bowled an incredible 10 overs straight at the Brisbane venue to snare 4-16 to restrict Bangladesh after they were asked to bat first in the third and final ODI.
The 33-year-old Schutt, who bowled 53 dot balls in her spell, took her series haul to 10 wickets at a miserly average of 7.1.
She now has 28 wickets in 14 ODIs at her favourite venue, the most of any bowler in history.
"She has had a pretty rough 12 months in the fact that she has been in and out of the side but you give the new ball to Schutter, you know she is going to do the job - either hold down an end or take poles, and she had an unbelievable series," McGrath said.
"It was awesome to see her back in an Aussie shirt and awesome to see her dominate."
Schutt has made a habit of taking early wickets in this series and she was at it again when removing Murshida Khartun (one) courtesy of a slick catch by Georgia Wareham in the gully in the third over.
Sarmin Sultana (six) hooked Schutt straight down Alana King's throat and then in-form duo Nigar Sultana (three) and Sobhana Mostary (nine) both fell to the speedster.
Sharmin Akhter (50) played a classy knock and enjoyed great support from 19-year-old allrounder Shorna Akter, whose 54 off 71 deliveries was her highest in ODIs.
Akter was dismissed by a brilliant stumping by wicketkeeper Mooney in her milestone match.
"We got a lot of experience," Akhter said.
"We were playing against Australia in Australia for the first time but we learned a lot of things which will be good for us in the next series in New Zealand."
McGrath said it was "awesome" for Australia to win the series.
"The squad is in a really good mood," she said.
Earlier, opener Phoebe Litchfield was ruled out of the match with a low grade hip strain.
The star batter was replaced in the side by allrounder Nicola Carey.
Litchfield has been in elite form in the series, which Australia leads 2-0, with innings of 77 and 70.
During the latter knock on Sunday night Litchfield appeared to suffer the hip complaint and called for a trainer before continuing her innings.
She will be monitored ahead of the three-game T20 series against New Zealand which starts in Sydney on Tuesday.
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