The poll, conducted by Fox News from September 25-27, gives Romney the lead with 23 percent support to Perry's 19 percent. Herman Cain, who won Florida's straw poll last weekend, trailed Perry by just two points, with 17 percent support -- reflecting a big boost for the former Godfather's Pizza CEO.
Michele Bachmann, meanwhile, continued her race to the bottom with just three percent support (down from eight percent in August), trailing former Utah Governor Jon Huntsman by a point.
In a survey conducted by Fox less than a month earlier, Perry stood at 29 percent, with Romney at 22 percent. During the same period, Cain has nearly tripled his strength; as of August, the poll found he had just six percent support.
Romney was widely considered the Republican frontrunner for the Republican presidential nomination until August, when Perry jumped into the race as a late entrant. Since then, the two have been neck-and-neck in most polls - usually with Perry eking out a slim lead over the former Massachusetts governor.
But after a series of Republican presidential debates in which Perry struggled, the Texas Republican appears to be losing some traction among voters.
"He needs to regroup," said University of Virginia political analyst Larry Sabato, in an interview with the Texas Tribune. "He's so uneven. He's done well sometimes, poorly others. It's unusual that you have a candidate who does show such a disparity in performance. I think part of that is exhaustion."
"Saturday Night Live" has taken to mocking Perry's debate performances; in its season-opening episode, a sketch depicts a mock-Perry getting flustered and incoherent over the course of a debate.
"This is normally when you get tired and confused," the moderator tells the Perry character at one point.
Meanwhile, Romney continues to lead Perry in hypothetical match-ups against President Obama: According to the Fox poll, Mr. Obama had a three-point lead over Romney among all registered voters. When pitted against Perry, Mr. Obama led by eight points.