Love said in a statement that the support is "encouraging."
"Sadly, Jim Matheson has turned to false attacks on my community and my family. Now is the time for Jim Matheson to stop his negative campaign," she said.
Love, who talks about her parents' emigration to America from Haiti at every speaking opportunity, blames Matheson for questions raised about their path to citizenship.
On Tuesday, Love and her campaign refused to answer a series of questions about her parents' story.
The Matheson campaign said releasing the poll is an attempt by Love's campaign to do damage control.
"It's a totally biased internal poll and given the bad week and bad day our opponent had it seems like an attempt to get control of her flailing campaign," said Matheson spokeswoman Alyson Heyrend.
The POS poll of 400 likely voters was conducted on Sept. 10 and 11 two-and-a-half weeks after ads hit the airwaves in the race and has a margin of error of 4.9 percent.
The poll also showed Love's favorability climbing and Matheson's falling from 68 percent to 57 percent. It also found Mitt Romney leading Barack Obama in the district, 73-25.
Robert Gehrke Twitter: @RobertGehrke