The overhaul was approved by a 81-17 vote Thursday and now sets the stage for what could be contentious negotiations with the House over the federal government's influence over education policy.
A week ago, the House passed its own update of the 2002 law that President George W. Bush pushed.
The Senate bill would leave in place the law's annual testing schedule. But senators voted to give states and districts more control over whether and how to use tests to assess the performance of schools, teachers and students.
It's a more moderate approach than the House bill.
The chambers will have to negotiate and approve a compromise.