The businessman comes out ahead of Hillary Clinton by just three points, 45-42, among likely Texas voters, with Libertarian Gary Johnson following at 7 percent and Green Party candidate Jill Stein at 2 percent.
Another Texas poll released this week, from Crosswind/Austin American-Statesman, showed Trump with a bigger, seven-point lead, 45-38, with Johnson at 7 percent.
University of Texas/Texas Tribune has not polled Lone Star State voters on the general election.
The University of Texas/Texas Tribune poll was conducted online by YouGov, surveying 959 likely Texas voters, with a margin of error of plus or minus 3.16 percent.
TPM's PollTracker Average for the general election in Texas shows Trump leading Clinton, 45.7 to 41.