Displaying a brand of ruthlessness that swept Coetzer off the court, Hingis won in straight sets - 6-1, 6-0 - in 47 minutes at Burswood Dome.
Coetzer, 29, ranked 11th, fought gallantly against the 20-year-old superstar, but had no answer to her power serving and precision returns.
Switzerland's Roger Federer had a chance to clinch his country's final spot by winning the men's singles, in which he was about to come up against Wayne Ferreira.
The winner of the tie will clash with the United States' Monica Seles and Jan-Michael Gambill in the final.