Sutherland snared career-best figures of 4-46 with the ball - even while having four catches dropped off her bowling - as India were skittled for 198 on Friday.
In reply, Australia were in trouble at 3-58 before Sutherland (20no off 29 balls) and Ellyse Perry (43no off 62 balls) combined to lift the home side to 3-96 by stumps.
Sutherland is just 24 years old but has already notched 52 ODIs and 48 T20s for her country.
She's now featuring in her seventh Test, with her highest score being the 210 she posted against South Africa at the WACA two years ago.
The way Sutherland was able to bowl through 36C heat on Friday before backing up for a crucial stint with the bat amazed her teammates.
"She's definitely the high-performing athlete that everyone dreams to be," Test debutant Lucy Hamilton said.
"And knowing that she does both with bat and ball and under the composure and the skill-level she does, it's a real testament to her.
"Being on the field and watching her do her thing was really cool.
"And being in gully, watching it fly through to Moons (wicketkeeper Beth Mooney) - unbelievable from her."
Jemimah Rodrigues, who made 52 for India, was also full of praise for Sutherland, who's been a teammate of hers at Delhi Capitals.
"I mean, she's one of the best all on allrounders going around," Rodrigues said.
"And watching her so closely in DC, I think she's very professional with her work.
"She's well-prepared always, and just knows her plans, very sorted, very calm head on her shoulders."
Australia captain Alyssa Healy fell for 13 in the first innings.
But the retiring great will hopefully get one more chance to bat later in the match.
Along with Sutherland, Hamilton also wrought havoc with the ball on Friday, snaring 3-31 in her Test debut.
She said snaring the first wicket of the match - a beautiful delivery that bowled star India batter Smriti Mandhana - gave her huge confidence.
"It was really special," Hamilton said.
"Getting the first wicket of the game was a tick in my box.
"And to do my job and come on for a second spell and impact the game was really nice, and what a fast bowler always wants to do."
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