The measure now goes to President Obama for signature.
The United States hit its $16.4 trillion borrowing limit New Year's Eve and since then the Treasury has been using what Secretary Timothy Geithner called "extraordinary measures" to pay the nation's bills. That ability, he had warned, would run out before the middle of March.
The suspension, approved 64-34, runs through May 19, at which point the debt limit will be reset at a higher level. Extraordinary measures then can be reinstituted to carry the issue into August.
The Bipartisan Policy Center estimates the United States will run up an additional $450 billion in debt before mid-May, The Washington Post reported.
Though a debt ceiling crisis has been averted for now, Congress still needs to deal with the sequester, which kicks in March 1, imposing a series of across-the-board spending cuts that hit the Pentagon especially hard. Also looming is the March 27 expiration of a broad government funding bill, posing the threat of a possible shutdown.
The suspension bill also requires the Senate to produce a 2014 budget or face suspension of members' paychecks.