The poll said Cain's success in recent debates appears to have boosted his support to 27 percent of potential Republican primary voters, up 22 percentage points from six weeks ago. Romney maintained his 23 percent support, while Perry's support fell from 38 percent at the end of August to 16 percent last week, the Journal said Thursday.
The newspaper said Cain received strong support among college-educated males, Tea Party backers and those who consider themselves "very conservative." The poll said Romney's strongest support was from those who see themselves as moderate to liberal Republicans.
Perry saw particularly sharp drops in support among men and voters older than 55, and his Tea Party support dropped to 15 percent from 45 percent in August.
The poll suggests Romney has the strongest chance of beating President Barack Obama, trailing the president 46 percent to 44 percent.
The poll of 1,000 adults, conducted Oct. 6-10, has a margin of error of 3.1 percentage points.