A University of Texas/Texas Tribune poll found that 47 percent of voters back Abbott, while 36 percent say they'd vote for Davis. The poll found that 17 percent had no opinion on who they'd vote for in the November election.
The new poll shows the Republican attorney general gaining momentum in the historically red state of Texas. In October, the same poll found Abbott with a six-percentage-point lead over Davis.
Both candidates have found themselves in hot water on the campaign trail recently. Davis came under fire earlier this year following the publication of a Dallas Morning News profile that prompted critics to accuse her of exaggerating her rags-to-riches story.
Davis rose to national fame last year during her state Senate filibuster on abortion.
Abbott has taken heat in the last week for appearing at campaign events with Ted Nugent. The shock rocker, who made two campaign appearances last week with Abbott, called President Obama a "subhuman mongrel" last month and ultimately was forced to apologize. Abbott has been criticized by both Republicans and Democrats for embracing Nugent at campaign events.
The poll released Monday has a margin of error of plus or minus 2.83 percentage points. It was based on an Internet survey of 1,200 registered voters and was conducted between Feb. 7 and Feb. 17, the Tribune reported.