After losing the toss and being sent in to bat in 36C heat on Friday, India went to tea struggling at 4-99, with Jemimah Rodrigues (15no) and Deepti Sharma (4no) at the crease.
Debutant left-arm pace bowler Lucy Hamilton (1-23 off seven overs) snared the first wicket of the day when she bowled Smriti Mandhana for four in the sixth over, sparking wild celebrations.
But Sutherland was the stand-out bowler of the opening session, snaring 2-26 from six overs in a spell that could have easily netted four or five wickets.
The 24-year-old found the edge of Shafali Verma's bat to send the opener packing for 35 off 48 balls.
Sutherland had her second wicket when Hamilton took a sharp catch at third slip to dismiss Pratika Rawal for 18.
It was just reward for Sutherland, who could only watch in vain as Rawal (on four at the time), Rodrigues (on 0) and captain Harmanpreet Kaur (on 10) were all put down off her bowling.
Harmanpreet was eventually out for 19 when bowled by Darcie Brown, leaving India 4-84 before they safely negotiated the rest of the opening session.
Star all-rounder Ellyse Perry, who missed all three ODI matches of the multi-format series with a quad niggle, was selected for the Test, but as a batter only.
Hamilton, 19, was included after Kim Garth was ruled out with a quad injury, while incoming captain Sophie Molineux (back) was another big name to be ruled out.
The four-day match marks the final international appearance for Australia skipper Alyssa Healy, with the 35-year-old slated to bat at No.4.
India named four debutants, including three pace bowlers - Sayali Satghare, Kranti Gaud and Kavshee Gautam.
Their other debutant is Rawal.
Star India quick Renuka Thakur was ruled out of the Test as part of a management plan for her workloads.
Australia lead the multi-format series eight points to four, meaning India must win the Test to come away with a draw.
