WASHINGTON—A federal appeals court Friday invalidated an array of voting restrictions North Carolina imposed in 2013, finding that they violated the Voting Rights Act by obstructing African-Americans’ access to the polls.

In a blistering opinion that minced few words about the racial polarization it said continues to afflict the state, the Fourth U.S. Circuit Court of Appeals in Richmond, Va., reinstated an array of election tools that disproportionately aided African-Americans. The court said Republican lawmakers had eliminated...