The latest poll results come as Clinton returned to Ohio Monday to campaign in person for the first time since Labor Day. She was in Toledo and Akron.
In Florida, Clinton now holds a 5 percentage point lead, in Pennsylvania she is ahead 4 points and in North Carolina her lead is 3 points. In a previous poll by Quinnipiac University, Clinton and Trump were deadlocked in Florida.
“Although Hillary Clinton clearly won the first debate with Donald Trump, this victory did her only little good in her race for the White House,” said Peter Brown, assistant poll director, in a written release.
The poll found that half of Ohio likely voters think Clinton won the first debate held a week ago at Hofstra University.
Pollsters surveyed likely voters in live interviews on land lines and cell phones from Sept. 27 to Oct. 2. It has a margin of error of plus or minus 4.4 percentage points in Ohio and North Carolina and 4.2 percentage points in Florida and Pennsylvania.
Other highlights of the poll:
* Trump is leading Clinton 58-31 percent among men in Ohio.
* Clinton is leading Trump 51-39 among women in Ohio.
* Trump leads Clitnon 52-33 among independent voters in Ohio.
No Republican has ever won the White House without carrying Ohio and the last Democrat to do so was John F. Kennedy in 1960.
Meanwhile, Ohio Secretary of State Jon Husted announced Monday that requests for absentee ballots are running higher this year than for the 2012 presidential election. So far, 957,260 absentee ballot applications have been received, compared with 922,199 received at this point in 2012.
The deadline to register to vote in Ohio is Oct. 11 and absentee voting and in-person early voting starts Oct. 12.