In a sign of the importance of the state for him, Romney appeared together with his vice presidential nominee, Paul Ryan.
Romney, appearing after country singer Trace Adkins energized the crowd, said the debate offered two different visions for the country.
"What you didn't hear last night from the president is why it is the next four years are possibly going to be better than the last four years. He doesn't have a way to explain that, because he has the same policies for the next four years as he had for the last four years," Romney said.
The debate win was badly needed by Romney, whose poll numbers had dropped in recent weeks after several missteps and the release of a damaging video showed him disparaging 47 percent of the electorate as dependent on government aid.
Going into the debate, Obama held a lead of 5 to 6 percentage points over Romney in most national polls, and is ahead by at least narrow margins in almost all the battleground states where the election will be decided.
But Romney is now viewed positively by 51 percent of voters, the first time he has enjoyed a net positive in the presidential race, according to a Reuters/Ipsos poll taken after the debate. Obama's favorability rating remained unchanged at 56 percent.