Likely voters favored Romney in the presidential race by 49 percent to Obama's 45 percent, while Romney came up even at 46 percent with Obama among registered voters, Pew said. Romney had trailed Obama by nine points among likely voters in September.
Other polls found that Romney got a bump from last week's debate, the first of three presidential debates, but most showed Obama retaining the lead.
A Reuters/Ipsos poll on Sunday, for example, found 47 percent of likely voters saying they would vote for Obama and 45 percent for Romney if the November 6 election were held now.
The Pew Research Center for the People & the Press survey of 1,511 adults, including 1,201 registered voters, conducted October 4-7 found that voters by almost three to one said Romney did a better job than Obama in the October 3 debate.
"Romney is seen as the candidate who has new ideas and is viewed as better able than Obama to improve the jobs situation and reduce the budget deficit," said Pew in a statement.
Romney's favorable rating rose five percentage points in September to hit 50 percent among registered voters for the first time in Pew Research Center surveys, it said.
Romney also achieved gains over the past month among women, white non-Hispanics and those younger than 50, said Pew. It noted that likely women voters are now evenly divided at 47 percent each for Obama and Romney, when last month, Obama led Romney by 18 points among women likely to vote.
This week, the focus of the campaign shifts to the debate on Thursday between Vice President Joe Biden and the Republican nominee to replace him, Wisconsin Congressman Paul Ryan.