The House earlier had voted to also create a GOP majority on the Legislative Management Committee, which hires staff, sets schedules and allocates budgets.
The Senate did not agree to the second committee change and passed the amended HB220 on a 21-7 vote. The House later agreed to the Senate changes, and send the amended bill to Gov. Gary Herbert for his possible signature.
Sen. Margaret Dayton, R-Orem, Senate sponsor of the bill, noted that Republicans have more than 80 percent of members in the House and Senate, and said they have earned the right to have bigger majorities on all committees.
"This is a bill that's promoting principle and proportionality and the true voice of the people," she said.
But Senate Democratic leader Gene Davis, D-Salt Lake City, said the current equal membership on those committees was created 40 years ago when the Democrats held the majority, so that management of the Legislature would not be used as a partisan weapon.
Sen. Jim Dabakis, D-Salt Lake City, said the change is "kind of insulting to Democrats."
Sen. Lyle Hillyard, R-Logan and the longest sitting legislator, opposed changes, saying the current bipartisan makeup of the two panels forces leaders to talk through issues to ensure fairness.
"If we can simply power things through because we have a majority vote without sitting down and talking about those issues, then I think we are doing ourselves all a great disservice," he said.
All other legislative committees already are controlled by lopsided Republican majorities.