Consumers can press ahead with a lawsuit that accuses Apple Inc. of using its market dominance to artificially inflate prices at its App Store, the U.S. Supreme Court ruled May 13.

The 5-4 decision could add to pressure the company faces to cut the 30% commission it charges on app sales. Lawyers pressing the case have said they will seek hundreds of millions of dollars on behalf of overpaying consumers.

Apple contended the lawsuit was barred under a 1977 Supreme...