The 16-year-old Russian was runner-up in the junior girls at Melbourne Park last year and reached the fourth round at Wimbledon to rocket into the world's top 50.
Andreeva looked every inch a superstar on the rise on Wednesday as she sent Jabeur packing 6-0 6-2 in just 54 minutes.
Her victory set up a third-round encounter with Frenchwoman Diane Parry, a 7-5 6-2 winner over Russian Kamilla Rakhimova.
It was Andreeva's first win over a player ranked inside the top 10.
"I was really nervous before the match because I am really inspired by the way (Jabeur) plays," Andreeva said.
"Before I started to play on the WTA Tour I always watched her matches, and now I got the chance to play against her.
"Honestly, in the first set, I played amazing tennis - I didn't expect that from myself."
Andreeva's pre-match preparation included encounters with a koala and snake in a meet-the-animals session at Melbourne Park on Tuesday.
"I held the snake, I did it with my agent," she said.
"He was so scared, but I forced him to do it."
Despite being a fixture in the top 10 for several years, Jabeur is still seeking a maiden grand slam singles crown.
The Tunisian has lost the past two Wimbledon deciders, and also came up short in the 2022 US Open final to Iga Swiatek.
The 29-year-old has never gone beyond the quarter-finals in seven visits to Melbourne Park.
She had also never been beaten so heavily in a grand slam career covering 80 matches as she was by Andreeva.
Another less celebrated Russian youngster, qualifier Mari Timofeeva, caused a second boilover early on Wednesday.
Timofeeva, 20, overcame a slow start to end the challenge of former world No.1 Caroline Wozniacki 1-6 6-4 6-1.
Mother-of-two Wozniacki, playing the fifth tournament of her comeback, joined fellow former Open winners and mums Naomi Osaka and Angelique Kerber on the sidelines.
After a fast start, Caroline Wozniacki could not keep the momentum going against Maria Timofeeva. (Joel Carrett/AAP PHOTOS)
Timofeeva's third-round opponent will be either another Russian qualifier, Alina Korneeva, or No.10 seed Beatriz Haddad Maia from Brazil.
"I'm really a bit speechless," Timofeeva said.
"It's an honour play here against Caroline.
"I went into the match without any expectations, just wanted to show what I was capable of."
The clash between Danish legend Wozniacki and Timofeeva under the roof on John Cain Arena was the only match to begin at 11am (AEDT) on Wednesday as heavy overnight and morning rain pushed back the start of play on the outside courts.
Play on the other show courts began at midday, with world No.4 Coco Gauff winning her all-American affair with Caroline Dolehide 7-6 (7-2) 6-2 in an hour and 44 minutes.
Dolehide faltered against the 19-year-old star while serving for the first set at 6-5, before the wheels came off in the second.
Gauff has never been past the fourth round at Melbourne Park and is playing her final grand slam as a teenager, having reached the 2022 French Open final, before winning the 2023 US Open crown.
"I wasn't nervous today," she said.
In other results, fellow Americans Alycia Parks and Amanda Anisimova respectively upset Canadian 32nd seed Leylah Annie Fernandez and Argentine Nadia Podoroska in straight sets.
And Czech world No.11 Barbora Krejcikova belted German Tamara Korpatsch 6-2 6-2.
