Local hope Stosur had upset former world No.1 Angelique Kerber to progress beyond the first round for just the second time in seven years on Monday.
And the veteran started well against the eighth seed and 2017 US Open finalist by grabbing an early break on Wednesday.
But the American responded with a break of her own, and applied the pressure again in the 12th game to seal the first set.
Keys broke serve again to begin the second, sealing victory in 77 minutes with 10 aces to her name in a win that improved a career 0-3 record against 2011 US Open champion Stosur.
“Sam obviously has a great serve and a great forehand and she’s really tricky off of her slice,” Keys said. “So I’ve known that in the past; I just felt like in the past I wasn’t doing a great job at handling my side of the court.”
Stosur will continue her Australian Open preparation at the Hobart International.
Collins now faces Key in an all-American quarter-final showdown.
The pair were once pen pals after meeting on the junior circuit, Keys describing Collins’ hot form as a “joke”.
“She’s playing incredibly well, really ripping and going for shots. And she’s making pretty much all of them right now,” she said.
Australian world No.1 Ashleigh Barty won’t begin her singles campaign until Thursday but is already just one win from the doubles final.
The 23-year-old will play Jennifer Brady in the second round, in the first match on Pat Rafter Arena on Thursday.