Serena Williams came from a set down to oust 2017 champion Sloane Stephens 2-6, 6-2, 6-2, in what she called an "intense" encounter on Arthur Ashe Stadium.
The nine-team US circuit will stage its 45th campaign at The Greenbrier in White Sulphur Springs, West Virginia, from July 12-August 2.
Japan's Naomi Osaka retained the world number one spot.
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.