The tournament hosts were staring at an early exit after crashing to 3-10 in reply to Sri Lanka's 6-122.
Australia were off to a good start to their chase with opener Alyssa Healy (51) making a 35-ball 51 laced with six boundaries and a six to anchor the chase initially.
Jemimah Rodrigues contributed useful 26 runs off 33 balls.
England's total of 176 for two, after being sent in to bat, was the side's highest T20I total and Knight's unbeaten third-wicket stand of 169 with Natalie Sciver (59 not out) was the highest partnership for any wicket in Women's T20 World Cup history.
Rodrigues was trapped leg before just as India were about to mount their final assault, she chose to review but the decision was upheld giving Delissa Kimmince her first wicket.
"We've had a lot of experience playing in front of our home crowd and it was a great atmosphere", she said.
Astronaut Christina Koch reunited with her dog after year in space
She also said it's good to be back home and she is enjoying her favourite things from food to hanging out at the beach. As the pooch smothered her with love and affection, giving kisses, Koch too was overwhelmed to see the dog's reaction.
However, when Healy and Lanning (5) fell to spin, Australia's innings unravelled, with Perry out for a golden duck and India's victory sealed when Megan Schutt was run out from the penultimate ball of the match.
Perth, Feb 23 (SocialNews.XYZ) India need to be measured and avoid complacency in their match against Bangladesh in the 2020 ICC Women's T20 World Cup, according to batter Veda Krishnamurthy.
"It was a challenging game for us today, but we tried our best", said Thai captain Sornnarin Tippoch.
"It's sometimes hard to keep your standards so I thought we did that well".
Aussies to Win the #T20WorldCup after that win me thinks ...!
India face Bangladesh in their next Group A match on Monday and would be hoping that Poonam replicates the performance she put out against the four-time champions and proceed towards their first-ever ICC title.
India: 132 for 4 in 20 overs (Deepti Sharma 49, Shafali 29; Jess Jonaseen 2/24). I'll be on her back in the next few days as it's normally her up the other end outscoring me.