WASHINGTON  An arms control treaty paring back American and Russian nuclear arsenals won a decisive vote in the Senate on Tuesday, clearing it for final approval and handing President Obama an important foreign policy victory.

The Senate voted 67 to 28 to end debate on the treaty, known as New Start, mustering the two-thirds majority needed for ratification despite a concerted effort by Republican leaders to sink the agreement. Eleven Republican senators joined every Democrat present to support the treaty, which now heads to a seemingly certain final vote of approval on Wednesday.

The outcome was another bipartisan victory for Mr. Obama, who emerged politically wounded from last month’s midterm elections but then successfully pressed Congress to enact several of his top priorities. At his behest, lawmakers passed an $858 billion package of tax cuts and unemployment benefits, and they ended the longstanding ban on gay men and lesbians’ serving openly in the military.

New Start was the last major challenge of the session for Mr. Obama, and in some ways it was the clearest assertion of his authority in the face of an emboldened Republican Party. The tax-cut deal required the president to swallow a compromise that extended the lower, expiring Bush-era tax rates even for the wealthy, alienating much of his own party. The overturning of the “don’t ask, don’t tell” military policy was driven in the final days as much by senators as by the White House.