It's proving to be a breakthrough season in the 23-year-old's blossoming career, with the 5-7 7-5 6-4 victory over former US Open champion Stosur another highlight.
Currently ranked 136, Inglis is eyeing a top-100 berth after chalking up her first WTA tour win at the Phillip Island Trophy earlier this month and then backing it up against Stosur.
She also pushed Australian Open defending champion and fourth seed Sofia Kenin in their round-one clash at Melbourne Park before falling 7-5 6-4.
"I'm obviously stoked to get the win," Inglis said.
"I could see Sam wasn't 100 per cent in the third set so I think I got a bit lucky in the end but it's pretty special to play against Sam as she was an idol growing up and someone I've always looked up to.
"To be on the same court as her was a really cool experience."
Inglis looked sharp in the first set and served at 5-4 but tightened up and lost the next three games to hand Stosur the lead.
In an even affair, she took seven break points before landing a late break in the second set to lead 6-5 and this time was able to level the match.
Stosur left the court for treatment for an issue with her leg that appeared to be restricting her movement.
But the 36-year-old, who made the Australian Open mixed doubles final last week, hit the ground running to take a 3-0 lead in the third.
West Australian Inglis, however, showed great fightback to level at 4-4 and then broke Stosur again to wrap up a gutsy win in two hours 47 minutes.
Sanders broke wildcard Tomljanovic in her first service game of the match and never looked backed in a one-sided affair, winning 6-1 6-2.
Earlier, Swiatek accounted for American Madison Brengle 6-3 6-4.
As well as taking on the world No.18, Brengle battled a migraine and required a medical time-out to seek further assistance.
In other matches, 16-year-old American Coco Gauff beat Italy's Jasmine Paolini 6-4 6-7 (4-7) 6-2, Japan's Misaki Doi defeated Anna Blinkova 7-6 (7-5) 3-6 6-2 while Jil Teichmann was too strong for Kristina Mladenovic, winning 6-2 7-6 (7-5).