Australia went to lunch on day two at 5-366 - an overall lead of 290 - with Sutherland (113 not out) and Ashleigh Gardner (52no) at the crease.
Sutherland started play on Friday on 54, and she was rarely troubled as she made her way to triple figures.
It marked the second time she has scored a Test century, following on from her unbeaten 137 against England in 2022.
It was also the highest score in a women's Test at the WACA, beating the 112 posted by England's Janette Brittin in 1984.
Century for Sutherland! 💯— cricket.com.au (@cricketcomau) Already her second Test ton - and brought up in style!#PlayOfTheDay | @hcltech | #AUSvSA pic.twitter.com/fKDMTmTjk0February 16, 2024
Sutherland's heroics with the bat came just a day after she took 3-19 with the ball as the Proteas were skittled for 76.
"I love batting," Sutherland told the Seven Network after making another Test ton.
"It's pretty hard to get up the order at the moment in the white-ball stuff, so it's nice to get a chance to have a hit out there.
"It's a very nice place to bat when you're in and set.
"I was wary that the first 20 to 30 balls were the most challenging, so I was trying to be precise with what balls I was trying to score off and what balls were the danger balls."
Sutherland revealed her parents were in the crowd to witness her special moment.
"It's cool to spend some time with them," she said.
"I had dinner with them last night. I think they were stoked to be here and watch the team play."
Sutherland's joy was in complete contrast to Alyssa Healy's heartbreak late on Thursday.
With just four minutes remaining in the day, the Australia skipper was caught and bowled for 99, crushing her hopes of becoming the first woman to post an international century in all three formats.
Australia only need to draw the Test match to win the multi-format series against South Africa.
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