Stand-in captain Tahlia McGrath invited the visitors to have first use of Allan Border Field and Schutt struck with the first ball of the innings, a vicious lifter that had opener Fargana Hoque edging to slip.
A Schutt inswinger trapped Sarmin Sultana (four) in front and from that moment the bowlers kept a vice-like grip on the run rate and picked up steady wickets to dismiss Bangladesh for 166 with the fourth ball of the final over.
The wicket of Sultana was the milestone 150th for Schutt. Only legendary speed demon Cathryn Fitzpatrick (180) and current allrounnder Ellyse Perry (166) have more wickets for Australia in the format.
Schutt finished with 2-19 from her 10 overs with medium pacer Annabel Sutherland (4-30) proving a handful when she hit the pitch hard.
Spinners Ashleigh Gardner, Georgia Wareham and Alana King bowled with class.
The visitors had several cameos but nothing substantial. No.3 Sharmin Akhter made a classy and breezy 24, captain Nigar Sultana (29 off 86 balls) was brave but stodgy.
Veteran allrounder Ritu Moni (45 off 63) showcased her experience and nous and was the best of a mediocre bunch.
Schutt has relished playing at AB Field throughout her career, where she now has 20 wickets.
The quick was initially left out of the ODI side in February against India before a quad injury to Kim Garth opened the door for a recall.
Schutt took 5-19 at AB Field on that occasion to provide a timely reminder of her talents.
McGrath, usually a vice-captain, has been elevated to lead due to injury to regular skipper Sophie Molineux and rotated her bowlers with panache.
The opener of three ODIs at the same venue, Friday's clash is the first match of the summer on home soil for Australia's victorious T20 World Cup side since lifting the trophy in July.
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