Spinner Sophie Molineux finished with 2-20 from her four overs, but it was Schutt who proved the trickiest to handle.
Schutt snared the scalp of opener Vishmi Gunaratne for a duck in the third over to kick-start Australia’s dominant display.
The 31-year-old claimed another two wickets in the final over, lifting her overall wicket tally in T20 World Cups to 43.
That equals the mark set by South African Shabnim Ismail, who retired from international cricket last year.
The temperature soared into the mid-30s during the match, but Australia’s use of daily sauna sessions last month meant they were well prepared for what was to come.
“I think we’ve finally acclimatised, because I didn’t feel like I was going to die out there today,” Schutt said with a laugh.
“I think Mooney lost about 16kg out there. We’ve played in hot conditions before. We play a summer sport.
“It is what it is. You’ve got to suck it up and get on with it. The breeze out here made it a lot easier today.”
Nilakshi de Silva top-scored for Sri Lanka with an unbeaten 29 off 40 balls, while Harshitha Samarawickrama (23 off 35 balls) and Anushka Sanjeewani (16) were the only other batters to make it into double figures.
Australia opted against playing a fourth spinner, instead selecting fast bowler Darcie Brown.
The 21-year-old endured a tough outing, bowling three no-balls and a wide in her first and only over.
That meant that after just one legal delivery, Brown had figures of 0-10.
Brown finished with 0-12, and also dropped a simple catch in the field.
Georgia Wareham (1-21), Molineux and Ashleigh Gardner (1-14) were picked as Australia’s spinning trio, and they all performed well.
Australia’s run chase started in shaky fashion, with Healy clean bowled and Wareham run out via a brilliant direct hit from Kavisha Dilhari.
Australia, who are aiming for a fourth consecutive T20 World Cup crown, will be back in action on Tuesday when they take on New Zealand
AAP