The relatively smooth passage this time comes as most members of Congress face elections in November. Republicans have been less confrontational after a 16-day partial government shutdown last year sent their poll numbers sliding and chastened the party's conservative tea party faction.
A debt default could have shaken financial markets and spiked interest rates.
The quick action in the Senate on the debt contrasts with the lengthy showdowns last year and in 2012, when Republicans tried to use the critically necessary measure as leverage to win concessions from Obama.
Obama has been unwilling to negotiate over the debt limit since his re-election in 2012, and Wednesday's legislation is the third consecutive debt measure passed without White House concessions.
The Senate approved the measure by a near party-line 55-43 vote, with all of the votes of support coming from Obama's Democratic allies.
The measure is required so that the government can borrow to pay bills like pension benefits, federal salaries and payments to health care programs for the elderly and the poor.
The legislation would permit Treasury to borrow normally for another 13 months and then reset the government's borrowing cap, currently set at $17.2 trillion, after that.
Congress has never failed to act to prevent a default on U.S. obligations, which most experts say would scare financial markets.
Wednesday's vote exposed sharp divisions within the Republican Party. The leader of the tea party wing, potential 2016 presidential candidate Sen. Ted Cruz, tried to use a tactic known as the filibuster to prevent the bill from being put to a vote. That forced Republican leaders who opposed the delaying manoeuvr to join Democrats in casting a procedural vote to override it. Although all Republicans later voted against the legislation itself, the procedural vote could be detrimental to their careers.
The Senate's top two Republicans — both facing tea party challenges in party primaries this year — provided crucial momentum that led several other Republicans to switch their votes in solidarity.
The debt measure permits Treasury to borrow regularly through March 15, 2015, putting the issue off for the new Congress to handle next year.
Wednesday's vote safely clears away the debt issue before the Feb. 27 deadline set last week by Treasury Secretary Jacob Lew. The debt limit was reset to $17.2 trillion after a four-month suspension of the prior, $16.7 trillion limit expired last Friday. Lew promptly began employing accounting manoeuvrs to buy time for Congress to act.
Associated Press writer Andrew Taylor contributed to this report.