The Texas Politics Project poll released on Wednesday shows Abbott receiving support from 45% of voters. O'Rourke received support from 40% of the voters polled.
Many polls taken since July have shown Abbott with a 5 to 7 point lead.
Abbott holds a commanding lead over O'Rourke among white voters (58% to 29%), according to the poll. O'Rourke led Abbott in support from Black (71% to 15%) and Hispanic (52% to 33%) voters.
Gov. Abbott also led among male voters (53% to 36%) and voters 45 year old and older.
8% of the voters polled said they have not thought about the race enough to have an opinion. The Green Party's Delilah Barrios (2%) and Libertarian Mark Tippets (2%) also received support in the poll.
The Texas Politics Project surveyed 1,200 registered voters in Texas from Aug. 26 to Sept. 6. The margin of error for the poll is +/-2.83%.
Abbott and O'Rourke will meet for a debate at the University of Texas Rio Grande Valley in Edinburg on Friday, Sept. 30.