Anastasia Pavlyuchenkova beat Sloane Stephens 6-7 (3/7), 6-3, 6-3 to set up a last eight clash with Danielle Collins.
Three-time Grand Slam winner Murray only played six tournaments last season and arrived in Australia early to acclimatize and prepare.
Svitolina looked sluggish after playing the two longest matches in the tournament against Wozniacki and Bertens in the semi-finals.
Sloane Stephens said on-court coaching created a connection between players and fans.
Six-time champion Serena Williams shook off a sluggish start to power past eighth-seeded Karolina Pliskova 6-4, 6-3 on Tuesday and into the US Open semi-finals.
Anastasija Sevastova will face either 23-time major champion Serena Williams or eighth-seeded Czech Karolina Pliskova.
Novak Djokovic is vying to break through for a first Cincinnati Masters win after coming up empty in five finals.
In a gruelling 2hr 41min battle, French Open champion Halep prevailed 7-6 (8/6), 3-6, 6-4 over Stephens in a repeat of the duo's meeting in the final of Roland Garros earlier this year.
American third seed Stephens surged into Sunday's final against world number one Halep after overpowering Svitolina 6-3, 6-3 in the day's second semi-final.
Sloane Stephens, ranked a career-high third, suffered a first-round Wimbledon exit after falling to Simona Halep in last month's French Open.
Simona Halep is still waiting for a maiden Grand Slam title after three previous final defeats, while Sloane Stephens is the reigning US Open champion.
Simona Halep will have an opportunity to finally lift a Grand Slam trophy when she faces US Open champion Sloane Stephens in her third French Open final on Saturday.
Simona Halep reached her third French Open final where she will face US Open winner Sloane Stephens for the title.
French Open: Sloane Stephens produced a clinical performance to down Daria Kasatkina, the conqueror of world number two Caroline Wozniacki.
Simona Halep of Romania continued to lead the Women's Tennis Association rankings.
Sloane Stephens beat Jelena Ostapenko 7-6 (7/5), 6-1 to lift the Miami Open title for the first time.
Sloane Stephens will enter the top 10 for the first time next week when the WTA rankings are announced.
The United States duo of Shelby Rogers and CoCo Vandeweghe beat Belarusian duo Aryna Sabalenka and Aliaksandra Sasnovich to clinch Fed Cup crown for the 18th time.