By Kristina Peterson and Michael R. Crittenden 

WASHINGTON--The Senate passed a Republican budget for fiscal year 2016 early Friday morning after a grueling, round-the-clock marathon of amendment votes.

The conservative spending blueprint for the year that begins Oct. 1 marked the first GOP budget to clear the Senate in almost a decade and brought Republicans another step closer to passing a budget through both chambers.

The Senate adopted its budget in a 52-46 vote just before 3:30 a.m. Friday, with no Democratic support. GOP Sens. Ted Cruz of Texas and Rand Paul of Kentucky voted against it. Mr. Cruz is running for president in 2016 and Mr. Paul is expected to announce his own White House bid soon.

The House passed its own GOP budget earlier this week. Lawmakers are expected to merge the two spending blueprints and both chambers will vote on the unified budget after the coming two-week spring recess.

"By passing a balanced budget that emphasizes growth, common sense and the needs of the middle class, Republicans have shown that the Senate is under new management and delivering on the change and responsible government the American people expect," Senate Majority Leader Mitch McConnell (R., Ky.) said in a statement after the vote.

Democrats dismissed the GOP blueprint as ignoring the needs of middle-class Americans.

"You can see that at a time of massive income inequality, the Republicans believe that a rich get richer approach fits best," said Sen. Bernie Sanders (I., Vt.), the top member of the Democratic caucus on the Budget Committee.

The last Republican budget to pass the Senate was in March 2006, when former Sen. Judd Gregg (R., N.H.) led the Budget Committee.

Senate Republicans, who control 54 of the chamber's seats, had to maneuver carefully to pass a budget that needed 51 votes to be adopted. But Republicans expressed little doubt over the week that Mr. McConnell would find the needed votes.

Republicans have lambasted Democrats over the years for not always approving a budget when they were in the majority and were sharply aware of how it would look if they didn't pass their own, said Sen. Charles Grassley (R., Iowa.)

"We ran on a platform that if we are in the majority, we're going to have a budget," Mr. Grassley said.

Budgets are nonbinding and never become law, but they set the overall funding levels used to write spending bills considered later in the year. Top Republicans have said they plan to use spending bills to push GOP policies while avoiding the recent deadline-driven standoffs between Republicans and President Barack Obama.

If both chambers can pass a unified budget, Republicans can also tap into procedural shortcuts enabling them to bypass Senate Democrats on some legislation, potentially including a repeal of the Affordable Care Act, though Mr. Obama would veto it.

Senate Republicans said their budget will eliminate the annual federal budget deficit over a decade and curb spending by $5.1 trillion over that time. The Senate GOP budget is lighter on policy recommendations than the House budget adopted earlier this week, which includes more contentious proposals for overhauling Medicare and other federal safety-net programs.

Senate Republicans, of whom two dozen are up for re-election in 2016, opted to leave more policy decisions in the hands of committees.

Democrats said that Republicans would face criticism for supporting a budget that repeals the 2010 health law and shifts more responsibility to the states for Medicaid and food stamps.

"To have to own this entire budget is going to be a tough thing to write off," said Sen. Chris Murphy (D., Conn.)

Passage of the budget followed an hourslong slew of 44 amendment votes that began on Thursday at noon. Senate rules allow a budget to pass with just a simple majority, so to give the minority party a voice in the process, any senator can require a vote to be held on any amendment. The amendment votes are symbolic, but they can show momentum building for an issue.

Among the amendments passed as lawmakers continued to vote deep into the night was a measure from Sen. Brian Schatz (D., Hawaii) to give same-sex couples access to Social Security and VA benefits. Eleven GOP lawmakers voted with Democrats to pass the amendment.

"Gay couples legally married in any state should be entitled to veterans and Social Security benefits identical to any other married couples," Mr. Schatz said.

Many measures passed along or close to party lines, including one allowing states to opt out of Common Core education standards without a penalty. The academic standards are supported by former GOP Florida Gov. Jeb Bush, who is exploring a White House bid, but opposed by many conservatives.

The Senate unanimously passed an amendment from Sen. Mark Kirk (R., Ill.) to impose sanctions on Iran. Mr. Kirk's amendment comes as officials from a handful of world powers and Tehran have started a final round of negotiations to see if a framework agreement could be reached in the coming days. His amendment calls for sanctions against Iran that had been waived to be immediately reimposed if the White House cannot certify to lawmakers that Iran is complying with the terms of an agreement.

Write to Kristina Peterson at kristina.peterson@wsj.com and Michael R. Crittenden at michael.crittenden@wsj.com