"Republicans have shown that the Senate is under new management and delivering on the change and responsible government the American people expect," said Senate Majority Leader Mitch McConnell, R-Ky.
Democrats viewed the document differently, saying it relied on gimmickry and touted the wrong priorities.
"The budget we passed today is irresponsible and fails to effectively invest in our future," said Sen. Barbara Mikulski, D-Md.
The budget's solidly ideological tenor contrasted with a bipartisan bill the House overwhelmingly approved Thursday permanently blocking perennial cuts in physicians' Medicare fees. It too will wait until April for final congressional approval by the Senate, with McConnell saying his chamber will handle it "very quickly when we get back."
Read MoreObama claims the upper hand in budget fight with Congress
Though doctors face a 21 percent cut in Medicare fees April 1, the government can delay processing those payments until Congress' return. The measure, which also provides money for health care programs for children and low-income people, would be partly financed with higher premiums for top-earning Medicare recipients.
On the budget, only two Republicans voted no: Sens. Ted Cruz of Texas and Rand Paul of Kentucky, a pair of presidential hopefuls. Two other potential GOP presidential candidates, Sens. Marco Rubio of Florida and Lindsey Graham of South Carolina, voted yes.
All voting Democrats were opposed.
The Senate completed its budget work after enduring one of its more painful traditions: A multi-hour "vote-a-rama" in which senators repeatedly debate and vote on a pile of non-binding amendments well past midnight. Senators offer the amendments because the votes can demonstrate support for a policy or be used to embarrass opponents in future campaigns.
Those approved included one by Sen. Brian Schatz, D-Hawaii, entitling married same-sex couples to Social Security and veterans' spousal benefits. It got 11 GOP votes, including from several Republicans facing competitive re-elections next year.
Also adopted was one by McConnell aimed at thwarting Obama administration efforts to reduce coal pollution.
Congress' GOP budgets both matched the spending plan that Obama presented last month when it comes to defense, proposing $612 billion for next year, a 4.5 percent boost over current levels. Some conservatives were unhappy because they wanted more of the extra military spending to be offset with savings from elsewhere in the budget.