On a day when the temperature hit 40C in Perth, Australia reached 8-310 by dinner on day two in reply to India's 198, with Sutherland making 129 off 171 balls and Perry 76 off 116.
Although Perry missed out on making her third Test century, her score was enough to take her to 1006 Test runs - surpassing the previous Australian women's record of 1002 held by Karen Rolton.
That 16-year-old record was broken when Perry lofted spinner Deepti Sharma down the ground for four to move to 74 late in Saturday's opening session.
Perry now sits 10th on the all-time women's Test run scoring list.
Former England star Jan Brittin, who played 27 Tests until 1998, sits on top with 1935 runs.
But Perry can lay claim to being the only woman to have passed 1000 runs and taken more than 30 wickets.
Perry's knock was eventually ended when she was adjudged lbw on review at the hands of Sharma.
Sutherland and Perry's 128-run fourth wicket partnership moved Australia to a position of strength after the hosts had stumbled to 3-58 on Friday night.
The home side had another wobble as they went from 4-240 to 8-277 before tailenders Alana King (21no) and debutant Lucy Hamilton (12no) added valuable runs.
Sutherland walked to the crease on Saturday unbeaten on 20, and her love affair with the WACA continued as she whacked India's heat-stricken attack to all parts of the ground.
She'd hit 17 boundaries before her innings came to an end, caught at long-on off Sharma.
The 24-year-old's only other Test visit to the ground came two years ago when she cracked 210 in a comfortable win over South Africa.
Sutherland has now posted three consecutive Test centuries, with her 163 against England at the MCG last year sandwiched between her two big knocks at the WACA.
Her Test batting average now sits at an elite 89.37 midway through her seventh Test.
Sutherland also starred with the ball on Friday, snaring 4-46 while also having four catches dropped off her bowling. She now has 17 wickets at an average of 25.1.
India's sharp fielding ensured Australia's first-innings lead didn't blow out too much.
Jemimah Rodrigues took a sharp catch on Friday night to dismiss retiring captain Alyssa Healy for 13.
And she was at it again on Saturday, taking a ripping catch at short cover to send Beth Mooney on her way for 19.
Smriti Mandhana produced an even better effort at short leg when her cat-like reflexes resulted in a catch to dismiss Tahlia McGrath for 13.
Australia's collapse of 4-37 has at least boosted the chances of Healy having one final chance to bat in her farewell to international cricket.
18°C