The 410-13 vote demonstrates the House is committed "to a more responsible stewardship" of taxpayer dollars, said Rep. Dan Lungren, chairman of the Administration Committee.
The cut -- roughly $35 million -- would affect operating budgets for all House committees, leadership offices and individual member offices.
Speaking for the Democratic minority, Rep. Robert Brady, D-Pa., the ranking Democrat on the Administration Committee, urged his colleagues to support the bill, adding that he "looked forward" to finding additional cost-cutting measures.
Rep. Greg Walden, R-Ore., who led the transition team for Republicans, called the measure "a single step forward but it is a $35 million first step."
"We've got to grow the economy and create jobs and get Washington's fiscal house in order," Walden said. "This is a start."
He called the measure firm but flexible, telling lawmakers and agency leaders, "We will treat you as adults, but we will expect results."
Lungren said the measure was a "down payment for future efforts," explaining that he would keep the 5-percent reduction in place for 2012.
He also said he was talking to leaders of House offices to search for ways to cut their budgets without compromising their duties.
Rep. Harold Rogers, R-Ky., chairman of the House Appropriations Committee, said his committee will cut its budget by 9 percent.
"The Appropriations Committee is saying, 'We see your 5 and raise you 4,'" Rogers said.
"This day represents a crucial turning point for our nation as this new Congress begins a path to fiscal sanity," Rogers said. "With this resolution ... Congress will begin immediately to reduce spending. ... The first drawn blood is ours."