The chamber voted 21-14 for the measure, which is one of several bills pushed by the Idaho School Boards Association this legislative session.
Sen. Jim Patrick, R-Twin Falls, said he was confident school districts wouldn't cut salaries unnecessarily, over objections from foes who say it tips the balance of power of who gets to decide what teachers earn.
The measure now goes to the House for debate.
But one bill that isn't going to come to a vote is another ISBA-supported measure that gives school boards power to impose a "last, best offer" if contract talks with teachers stall. That legislation, which has been blasted by the Idaho Education Association teachers union, passed the House earlier this month on a 55-14 vote.
It would have given school board trustees power to end contract bargaining by June 10 if talks with teachers stall.
Sen. John Goedde, a Republican from Coeur d'Alene and the Education Committee chairman, said Friday he was asked by the ISBA to withdraw the bill.
ISBA Executive Director Karen Echeverria said she decided to nix it following concerns from senators who couldn't swallow passing bills giving school boards authority to cut teacher salaries and make the final offer in contract talks.
"There were senators who said they couldn't vote for both of those bills, so we decided that reducing salaries was most important to us," she said.
Echeverria said she has no plans to revive the legislation next session.
Hannah Furfaro in Boise contributed to this report.