Employers grappling with ways to lower their health-care costs are finding that earlier treatment for mental health can lead to better outcomes in the long run.

The sudden rise in opioid deaths, suicide, and autism are national issues, but more common mental health issues like depression and anxiety can be big liabilities for employers.

“The common prevalence of general mental illness like depression, stress, anxiety, in the American population is at an all-time high,” Suzanne Delbanco, executive director of the Catalyst for Payment Reform, told Bloomberg Law.

Mental health problems can be hard to detect when looking at medical claims,...