As polls showed Obama with a slight edge among voters, Romney was the aggressor throughout the 90-minute encounter between the two rivals at the University of Denver.
The two men, standing side-by-side for the first time after months of brutal campaign attacks hurled at each other, clashed over taxes, healthcare and the role of government, reflecting the deep ideological divide in Washington.
Appearing poised and well-prepared, Romney zeroed in on weak economic growth and 8.1 percent unemployment that has left Obama vulnerable in his effort to win a second four-year term.
"Now, I'm concerned that we're on the path that's just been unsuccessful. The president has a view very similar to the one he had when he ran for office four years ago, that spending more, taxing more, regulating more, if you will, trickle-down government would work. That's not the right answer for America," Romney said.
The debate saw no haymaker punches thrown and not much in the way of one-line zingers. Instead, it was a war of attrition as each man used facts and figures to make his points and stress the differences between them.
Romney, however, may have done himself some favors with crisper answers than Obama, who sounded professorial and a bit long-winded despite his staff's best efforts to get him to give snappier comments.
The incumbent Democrat did put Romney on the defensive about his proposals for overhauling the U.S. tax system.
Obama said Romney was promoting the same kind of tax cut proposals that former President George W. Bush pushed through Congress in 2001 and 2003.
"We ended up moving from surpluses to deficits and it all culminated with the worst recession since the Great Depression," said Obama.
In the face of attacks from Romney that the Obama healthcare overhaul of 2010 will hurt small-business hiring, Obama basically said his healthcare plan was modeled after the program Romney put in place as governor of Massachusetts, and it "hasn't destroyed jobs" there.
ROMNEY NEEDED VICTORY MORE
Romney was in need of a victory at the debate to help him put his campaign back on a positive footing after a rocky few weeks.
He was damaged by a hidden-camera videotape in which he said 47 percent of voters were dependent on government and unlikely to support him.
Obama, holding a slight edge in national polls and leading Romney in some swing states where the election will be decided, was looking in the debate to do avoid harming his position as the apparent front-runner.
The debate moderated by PBS anchor Jim Lehrer was the best opportunity to date to reach large numbers of voters in an unfiltered way, with an estimated television audience of 60 million possible.
Both men have been under pressure to provide more specific details on how to get America's economy surging again after a prolonged recovery from recession.
Obama charged that Romney's plan to reduce income taxes by 20 percent across the board and eliminate some tax deductions would leave middle-class Americans paying more taxes, an allegation that Romney vociferously denied.
"The fact is that if you are lowering the rates the way you described, Governor, then it is not possible to come up with enough deductions and loopholes that only affect high-income individuals to avoid either raising the deficit or burdening the middle class. It's - it's math. It's arithmetic," Obama said.
Replied Romney, "Virtually everything he said about my tax plan is inaccurate."
The debate was the first of three such face-offs scheduled in the next four weeks. Biden and Romney's running mate, U.S. Representative Paul Ryan, will also debate once, on October 11.
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