Ohio state senators narrowly approved a bill that would prohibit public-employee unions representing 400,000 state and local workers from bargaining over health benefits and pensions, while also eliminating the right to strike.

While national attention has focused for weeks on a similar battle in Wisconsin, the vote, by 17-16 in Ohio's Republican-controlled Senate, virtually ensured that the Buckeye State will become the first to strip collective-bargaining rights from public employees as states grapple with recent gaping...