The Quinnipiac University poll has 54 percent of Texans supporting Cruz and 45 percent for O'Rourke.
The poll also reveals that men back Cruz 62 - 37 percent as women tip to O'Rourke 52 - 46 percent.
Numbers from Sept. 28 showed O'Rourke leading by two points over Cruz from the Ipsos/Reuters/University of Virginia online poll.
SEE ALSO: Sen. Ted Cruz and Rep. Beto O'Rourke know turnout is key in Texas senate race
Among Texas likely voters who name a U.S. Senate candidate, 96 percent say their mind is made up, according to the Quinnipiac University poll.
Sen. Ted Cruz says 2018 reelection bid is 'a real race' with O'Rourke
Both candidates have been traveling across the Lone Star State to drum up votes, working overtime to drive their supporters to the polls.
"The single biggest challenge we have is complacency," said Cruz at a recent rally.
He told supporters they need to vote and ask the same of their family and friends.
"Now we need to finish the job," Cruz said.
Beto O'Rourke makes campaign stop at Prairie View A&M
This spring, Democrats had their highest number of voters in a midterm primary since 1994. It was nearly double four years ago but still lagged behind the GOP turnout by a half million voters.
O'Rourke has his work cut out for him despite the energy and turnout at his rallies, but he remains optimistic.
"This campaign being run without PACs, being run without special interests or corporations, all people all the time makes anything that we want to do possible," O'Rourke said in an interview with Eyewitness News. "We're bringing together everyone. We've been to all 254 counties, Republicans and Democrats alike welcome us at every single one of these meetings."