The vote was 221-201 after House Speaker John Boehner decided against a plan to tie the measure to restoring some cuts to military benefits adopted in the omnibus budget resolution.
The Senate was expected by the end of the week, averting possible default.
Boehner, R-Ohio, and Minority Leader Nancy Pelosi, D-Calif., stood on the House floor and shook hands as the measure passed with mostly Democratic votes. Only 28 Republicans supported the measure.
"Tonight's vote is a positive step in moving away from the political brinkmanship that's a needless drag on our economy," White House press secretary Jay Carney said in a statement. "The American economy is moving forward, but there is much more to do to ensure that more middle class Americans -- and those striving to get into it -- can get ahead. Congress can start by raising the minimum wage so that no one who works full time raises their family in poverty, restoring emergency unemployment insurance for the 1.7 million Americans searching every day for a job who need this vital lifeline to support their families, and taking additional steps to strengthen our economy and restore opportunity for all Americans. The president looks forward to working with both sides to get that done."
Boehner's decision earned the ire of the Senate Conservative Fund, which urged House Republicans to deny Boehner the speaker's post in January 2015, after the midterm elections.
The fund accused Boehner, R-Ohio, of "helping President Obama enact his liberal agenda," The Hill reported.
"Instead of using the House majority to stop bad legislation, Speaker Boehner has used it to increase spending, raise the debt limit, increase taxes, pass a bloated farm bill, and fund the implementation of Obamacare. Instead of fighting for conservative principles, Speaker Boehner has repeatedly surrendered to the Democrats," the fund said in a statement.
House leadership decided during a morning meeting to discard a bill that would have restored a cost-of-living raise for the military after the White House said raising the debt ceiling was not negotiable.
Boehner had said earlier Republican members would vote for a clean bill, but that Democratic support would have to assure its passage, the Washington Post reported.
Boehner's decision to bring only the clean bill up for a vote was met with "stunned silence" by others at the meeting, the New York Times reported.
Boehner had presented a plan Monday night that would have tied an increase to the debt ceiling to a reversal of cuts in military retirement benefits. The bill got no support from conservative Republicans and Republican leadership said support from Democratic members was unlikely.
Boehner's change of mind shocked GOP members because it violated the speaker's own "Boehner Rule" that increases in the debt ceiling had to be matched by equivalent cuts in the budget.
The president supported bipartisan efforts to reverse the military cuts, Gene B. Sperling, director of the White House National Economic Council, told reporters at a breakfast meeting.
However, he added, "I hope the tactic of threatening default for budget debates is over, off the table and never to happen again."
Treasury Secretary Jack Lew has said Congress must increase the treasury's borrowing authority or risk a U.S. default, beginning Feb. 27, on more than $17 trillion in federal debt.