CNN said 67 percent of 430 registered voters surveyed gave the win to the former Massachusetts governor, while 25 percent said the Democratic incumbent did the better job in the debate held at the University of Denver.
The poll also found 35 percent said the debate made them more likely to vote for Romney, while 18 percent said it made them more likely to cast their vote for Obama. Forty-seven percent said they were unswayed by either candidate, the CNN/ORC International Poll showed.
Fifty-three percent of the survey participants thought Romney spent more time attacking Obama, while 30 percent thought the president was the more aggressive debater.
When it came to who seemed to be the stronger leader, Romney held a 58-37 edge over Obama.
Sixty-one percent thought Obama did worse than expected, and 82 percent thought Romney did better than expected.
The poll, conducted by telephone, had a 4.5 percentage-point margin of error.