Barty made a quick begin and saved her cool after a mini second-set fightback from Rogers to safe the 6-3 6-4 win in 71 minutes on Monday night time.
The 2019 French Open champion will meet Czech world No.27 Karolina Muchova on Wednesday for a spot within the semi-finals.
Muchova beat Elise Mertens 7-6 (7-5) 7-5 to maneuver into the ultimate eight.
Barty’s progress means she’s the primary native hope to achieve three consecutive quarter-finals on the Australian Open since Wendy Turnbull made it 4 in a row in 1984.
“It’s actually thrilling to be by way of to a different quarter-final,” Barty stated throughout an on-court interview.
“If you happen to would have informed me a number of months in the past whereas we had been doing pre-season that that is the begin to the yr that we’d have, we’d completely take it with a large smile on our face.
“We come out right here and have enjoyable. I simply love being at residence, I like being in Australia and having the ability to share it with all my family and friends.”
Each gamers entered the match with out having dropped a set within the event.
Barty led the head-to-head battle 2-0, however their most up-to-date assembly earlier this month was a tricky encounter on the Yarra Valley Basic that was determined by a match tiebreak.
There was no crowd readily available to spur Barty on, however she was nonetheless in a position to make a quick begin to shoot out to a 4-1 lead.
Barty’s means to show a collection of defensive scrambles into offensive forehands proved essential.
She saved two break factors within the seventh recreation and didn’t give Rogers one other sniff on the best way to sealing the primary set in 29 minutes.
The unforced errors continued to mount for Rogers within the second set, with Barty snaring consecutive breaks to place her opponent on the brink at 5-1.
The one actual blemish for Barty got here when she was up 5-2 within the second and serving for the match at 40-15.
Barty dedicated a collection of unforced errors handy a break again to Rogers, however the Australian made amends in her subsequent service recreation to safe the win.
“I knew my serve was going to be large,” Barty stated.
“She’s a participant that may take the match away from you in a short time, so I wanted to have my trainers on. However I served properly and I attempted to be accountable for as many factors as I may.”