A divided Wisconsin Supreme Court has restored 82 appointees of then-Gov. Scott Walker who were confirmed during a lame-duck legislative session, handing a victory to Republicans and defeat to Democratic Gov. Tony Evers.

The 4-3 order on Tuesday affects 15 of the appointees who Mr. Evers hadn’t reappointed after a lower court said it was legal for him to essentially fire them. Mr. Evers argued the appointees were invalidated after a lower court ruled that the entire lame-duck session, where Republicans took powers away from...