The vote was 269-161, but all eyes were on Giffords, who drew thunderous applause as she walked into the House chamber unannounced and cast her vote in favor of the bill.
A final Senate sign-off for the measure is virtually assured on Tuesday.
"If the bill were presented to the president, he would sign it," the White House said, an understatement of enormous proportions.
After months of fiercely partisan struggle, the House's top Republican and Democratic leaders swung behind the bill, ratifying a deal sealed Sunday night with a phone call from House Speaker John Boehner to President Barack Obama.
"The legislation will solve this debt crisis and help get the American people back to work," Boehner said at a news conference a few hours before the vote.
The Democratic leader, Rep. Nancy Pelosi, was far less effusive. "I'm not happy with it, but I'm proud of some of the accomplishments in it. That's why I'm voting for it."
So, too, many of the first-term Republicans whose election in 2010 handed the GOP control of the House and set the federal government on a new, more conservative course.
"It's about time that Congress come together and figure out a way to live within our means," said one of them, Sean Duffy of Wisconsin. "This bill is going to start that process although it doesn't go far enough."
The measure would cut federal spending by at least $2.1 trillion over a decade - and possibly considerably more - and would not require tax increases. The U.S. debt limit would rise by at least $2.1 trillion, tiding the Treasury over through the 2012 elections.
Without legislation in place by the end of Tuesday, the Treasury would run out of cash needed to pay all its bills. Administration officials say a default would ensue that would severely damage the economy.
Beyond merely avoiding disaster, Obama and congressional leaders hoped their extraordinary accord would reassure investors at home and around the world, preserve the United States' Aaa credit rating and begin to slow the growth in America's soaring debt. In a roller-coaster day on Wall Street, the Dow Jones industrial average surged, then sank and finally finished down for a seventh straight session but only slightly.
In all, 174 Republicans and 95 Democrats voted for the bill, while 66 Republicans and 95 Democrats opposed it. After months of suspense, the vote was anti-climactic.
Not so the moment when Giffords' presence became known.
She greeted some fellow lawmakers who crowded around her and blew kisses to others, beaming the whole while. Her hair was dark and close cropped and she wore glasses - nothing like the image America had of her six months ago when she was shot while greeting constituents outside a supermarket in Tucson.
She did not speak with reporters.
As for the legislation, after months of wrangling over a deal, there was little time left for lawmakers to decide how to vote.
The White House dispatched Vice President Joe Biden to the Capitol to lobby recalcitrant Democrats in both houses.
"They expressed all their frustration," he conceded after a session with lawmakers of his party in the House.
He said the deal "has one overwhelming redeeming feature" - postponing the next debt limit battle until 2013 and putting the current fight behind. "We have to get this out of the way to get to the issue of growing the economy," he said.
Republicans lobbied their rank and file as well, and the results were far more positive for them than a week ago when they were forced to delay a vote on an earlier measure.
GOP leaders swiftly drew public pledges of support from some first-termers as well as veteran defense hawks - two areas of concern with the agreement.
Rep. C.W. (Bill) Young, chairman of the committee that handles the defense budget, said, "We're confident that we can make this happen without affecting readiness and without affecting any of our soldiers."
There were critics on both sides of the aisle, some of them anguished.
"I did not come to Washington to force more people into poverty," said Rep. Jim McGovern, D-Mass.
"At the end of the day, Washington's spending still has us sprinting toward a fiscal cliff. And this bill barely slows us down," said Rep. Mark Mulvaney, R-S.C.
There is little suspense about the outcome for the debt-limit legislation in the Senate on Tuesday.
A member of the Republican leadership in the Senate predicted strong GOP support. "Maybe 35 (of 47) will support it in the end. There will be some who will pull back," said Sen. Mike Crapo of Idaho.
Already, the legislation was emerging as an issue in the 2012 presidential campaign.
Rep. Michele Bachmann of Minnesota and former Massachusetts Gov. Mitt Romney announced their opposition, while Newt Gingrich issued a statement without saying how he would vote.
The final legislation reflected the priorities of the two political parties.
It would immediately increase the debt limit by $400 billion, with another $500 billion envisioned unless Congress blocks it. At the same time, it would cut more than $900 billion over 10 years from the day-to-day operating budgets of Cabinet agencies. For the budget year that begins Oct. 1, spending would be held $7 billion below current levels.
The measure also establishes a 12-member House-Senate committee that will be charged with producing up to $1.5 trillion in additional deficit cuts over a decade. If the panel succeeds, Congress will be required to vote on the recommendations without possibility of changes.
If the panel deadlocks or fails to produce at least $1.2 trillion in deficit savings, then spending cuts are to take effect across much of the federal budget. The Pentagon, domestic agencies and farm subsidies would be affected, as would payments to doctors and other Medicare providers. But individual benefits under Social Security, Medicaid, Medicare and programs for veterans and federal retirees would be exempt.
At the same time, the debt limit would rise by at least another $1.2 trillion, and perhaps - depending on the results of the committee's work - as much as $1.5 trillion.
Additionally, the legislation requires both the House and Senate to vote on a balanced-budget amendment to the Constitution.
The measure also increases funding for Pell Grants for low-income college students by $17 billion over the next two years, financed by curbs on federal student loan subsidies.
The result of weeks of negotiations and harsh arguing, the final result represented a product of divided government that gave neither side everything it wanted. Leaders in both parties were emphatic on that point.
"As with any compromise, the outcome is far from satisfying," conceded Obama in a video his re-election campaign sent to millions of Democrats. In a tweet, the president was more positive: "The debt agreement makes a significant down payment to reduce the deficit - finding savings in both defense and domestic spending."
Associated Press writers Jim Abrams, Stephen Ohlemacher, Alan Fram, Julie Pace, Donna Cassata, Andrew Taylor and Larry Margasak contributed to this report.