Vondrousova had beaten Arina Rodionova 6-0 6-0 in the previous round, showing encouraging form in her first tournament back after a wrist injury sidelined her for six months shortly after her French Open run.
Sabalenka will battle Dayana Yastremska on Friday for a place in the final after the Ukrainian 19-year-old beat a second top 20 opponent this week when she put out Croat Donna Vekic 6-4, 6-3.
In the first set, Halep twice lost break advantages, with Sabalenka coming through with a third break of serve in the final game on a double-fault from the seed.
"I didn't want to lose focus", said the world number 24, who has won three titles over the past two seasons.
In men's play, Canadian second seed Felix Auger-Aliassime swept the last 10 games to crush Australian wild card Alex Bolt 6-3, 6-0 in 54 minutes, losing just four points on serve during the rout.
"It's getting better and better", Barty replied when asked to assess her performance.
"If I can bring my "A" game, I believe in my chances".
There was a quarter-final shock for two-time Grand Slam victor Simona Halep, who heads into the Australian Open with room for improvement after being upset 6-4, 6-2 by Aryna Sabalenka.
Fourth seed Belinda Bencic came through a tight tussle with Julia Goerges to emerge a 7-6 (8-6) 7-6 (7-4) victor, with her last-eight opponent Danielle Collins having significantly less difficulty against fellow American Sofia Kenin - the unseeded 26-year-old winning 6-3 6-1.
Yastremska, ranked 24th, was thrilled to get past Vekic.
Elise Mertens remains on course for a third Hobart International title after the top seed dropped single game in her 6-1 6-0 defeat of Viktoria Kuzmova, setting up a quarter-final with Great Britain's Heather Watson, a 7-6 (7-5) 6-3 victor against Fiona Ferro.
"It's important that I have mental confidence", he said. "One day you still can play so good, the other day can be not that good".
"It's an awesome feeling to be top 20 for the first time, but there are still so many things that I can improve", he said.
Fourth seed Pablo Carreno Busta started with a 6-3, 6-2 defeat of Frenchman Jeremy Chardy.
South African qualifier Lloyd Harris also advanced to the quarters with a 7-6 (7/5), 6-3 win over Laslo Djere 7-6 (7/5), 6-3.