Three debates down. Two weeks of campaigning to go.

President Barack Obama put Republican challenger Mitt Romney on the defensive on foreign policy in the final presidential debate Monday night, with analysts and an immediate poll giving Obama the victory.

With 15 days before the Nov. 6 vote, the candidates now hit the road for the final sprint to Election Day -- focusing on the handful of vital battleground states that could decade the closely contested race.

Obama kicks off his "America Forward" tour Tuesday with events in Florida and Ohio, where he will be joined by Vice President Joe Biden, while Romney and his running mate, Rep. Paul Ryan, campaign in Nevada and Colorado.

In Monday's debate, Obama sought to highlight his experience after nearly four years leading the nation's military and foreign policy efforts. Romney, a former governor with less foreign policy experience, tried to paint Obama as an ineffective leader even as he expressed agreement with many of the administration's steps in Syria, Iran and other hotspots.

Analysts agreed that Obama won on points, but questioned if the result would have a big impact on voters and the race as a whole.

"There's no question debate coaches would score this one for the president," said CNN Chief National Correspondent John King, while CNN Senior Political Analyst David Gergen said Obama "dominated the middle of the debate" and emerged as the winner.

Both King and Gergen agreed that Romney avoided sounding like an overzealous advocate of military action -- which is how Obama and Democrats seek to portray him.

Alex Castellanos, a Republican strategist and CNN contributor, conceded Obama "won tonight on points, no doubt about it," but added that Romney showed the leadership style of a commander-in-chief to demonstrate that making a change in the White House would be safe.

A CNN/ORC International poll of people who watched the debate showed 48% favored Obama compared to 40% for Romney, numbers barely within the margin of error range of plus-or-minus 4.5%. Another poll by CBS scored it a clear victory for Obama.

At the same time, the CNN/ORC poll showed viewers thought Romney established credibility as a leader, which former White House Press Secretary Ari Fleischer, a Republican strategist and CNN contributor, said was very important.

"This isn't going to change the trajectory of the result," Fleischer said, noting that 24% of those questioned said the debate made them more likely to vote for Obama while 25% said it nudged them toward Romney, and 50% said they were not influence either way.

The poll also reinforced a gender gap in the race, with women favoring Obama as a strong leader by 59% to 39%, while men chose Romney by 53% to 43%. Obama needs to repeat the strong support from women voters -- who comprise half the electorate -- that helped him win in 2008.

The third and final face-to-face showdown occurred with the candidates running even in national polls and the race hinging on a handful of battleground states -- particularly Ohio, Florida and Virginia.

According to the latest polls, Obama has a slight lead in Ohio. Romney is ahead in Florida, and Virginia is a dead heat.

In the debate, Obama more than once sought to highlight Romney's lack of foreign policy experience.

The president took a jab at his challenger's world view -- paying him a backhanded compliment for his analysis of the threat of terrorism to the United States.

"Governor Romney, I'm glad that you recognize that al Qaeda is a threat, because a few months ago when you were asked what's the biggest geopolitical threat facing America, you said Russia, not al Qaeda; you said Russia," Obama said, adding that "the 1980s, they're now calling to ask for their foreign policy back because, you know, the Cold War's been over for 20 years."

Romney countered that in that speech, he had argued Iran was the nation's greatest security threat and identified Russia as a "geopolitical foe."

"Attacking me is not talking about how we're going to deal with the challenges that exist in the Middle East, and take advantage of the opportunity there, and stem the tide of this violence," he said.

Romney added that Obama's foreign affairs policies have made the United States less respected and more vulnerable, particularly as it relates to Iran.

"I think from the very beginning, one of the challenges we've had with Iran is that they have looked at this administration, and felt that the administration was not as strong as it needed to be," Romney said.

Romney also repeatedly tried to shift the discussion to his strongest issue -- the continued high unemployment and slow economic recovery under Obama -- arguing that a strong foreign policy and national defense depends on a strong economy.

"We want to end those conflicts to the extent humanly possible," Romney said. "But in order to be able to fulfill our role in the world, America must be strong. America must lead. And for that to happen, we have to strengthen our economy here at home."

Romney also accused Obama of supporting policies that undermine the nation's military preparedness.