the opening face-off in Denver, Colorado, the race is essentially up for grabs just three weeks before election day on November 6.
"I think the president had a much better night than he had in Denver," John Pitney, professor of politics at Claremont McKenna College, told AFP.
"It was close, but I have to give the edge to Obama."
Nearly all analysts said Romney mopped the floor with a dull and unfocused president two weeks ago, and Americans agreed; the challenger had been on the ropes after his controversial comments disparaging 47% of the electorate as government-dependent freeloaders, but he soared in post-debate polls.
But Obama, knowing he had to raise his game to have any hope of winning a second term, charged hard out of the gate in the 90-minute town-hall showdown, attacking Romney on his economic recovery plan and delivering a fiery retort to criticism of his handling of last month's Libya attack.
"It was a morale booster for the Democrats, and Republicans will find things to cheer too, but Obama needed the morale booster a lot more," Pitney said.
"We'll see if this moves the polls at all."
Several national surveys and polls in key political battlegrounds showed Romney wiping away his deficit in recent weeks, with some having him wresting the lead away from Obama.
But flash polls of debate watchers taken by three networks in the hour after Tuesday's encounter at New York's Hofstra University were unanimous in giving the president the advantage.
A CBS News poll showed 37% of respondents felt Obama won the debate, compared to 30% for Romney.
Karlyn Bowman, a senior fellow at the conservative American Enterprise Institute, said that while there was no clear winner, "Obama is back in the game."
The subject matter bounced from the economy to taxes and from energy to China, but women's issues loomed larger than in the first debate.
Support among women has been a mainstay for Obama, but it plunged in the aftermath of the first debate, according to several key polls.
Jennifer Lawless, head of the Women & Politics Institute at American University, said Obama would likely win women back after the debate, in which he offered them "the same fair deal as men."
"I wouldn't be surprised that following what happened tonight... we don't see the gender gap start to reemerge quite substantially," Lawless said.
The dispute over Libya, where US ambassador Chris Stevens and three other Americans were killed in September during an assault on the US consulate in Benghazi, gave Obama a chance to rebuke Romney over his continued criticism of White House's handling of the attack.
"The suggestion that anybody on my team, whether it's a secretary of state, our UN ambassador, anybody on my team, would play politics or mislead when we've lost four of our own, governor, is offensive," a glaring Obama said.
"That's not what we do. That's not what I do as president."
Pitney said Obama's response on the Libya issue crackled with passion and presidential mettle.
"The problem for the president is, he had a good moment on Libya, but Libya is not a good issue for the president," he said, referring to the conflicting accounts of the attack given by US officials in the days after it took place.
Linda Fowler, a professor of government at Dartmouth College, said there was no outright winner or loser at the Hofstra debate.
"They each did things they had to do, and this has been a close race and it will continue to be a close race," Fowler said.
"I think the Republicans will be disappointed that Romney didn't put him away, and the Democrats will be reassured that the president is in full press now."
Political science professor Steffen Schmidt of Iowa State University said the two candidates "really went at each other on oil and gas and energy," as well as tax policy.
But even as Obama called out Romney over his lack of specifics on how he would pay for his 20% tax cut, Schmidt said there was no stand-out winner.
"No independent undecided voters were probably moved to support either of them," Schmidt said.
"We need another debate to get this all straightened out."
Obama and Romney meet for their third and final showdown on October 22, 15 days before the election.