Cruz, the Republican incumbent, and O'Rourke, a Democratic congressman from El Paso, were on track to easily capture their parties' nominations Tuesday night, according to early returns.
Cruz, who is seeking a second term, was besting four little-known challengers with 84 percent of the vote, while O'Rourke was at 63 percent in a three-way nominating contest.
The results cement a general election battle that has raised the hopes of Democrats, who have a well-funded, hard-working candidate in O'Rourke. Still, O'Rourke has an uphill battle in a state where Democrats have not won statewide office in over two decades.
Until recently, Cruz had not done much to engage O'Rourke, ignoring him on the campaign trail. That changed in the final hours before polls closed Tuesday evening, when Cruz issued his most scathing critique of O'Rourke yet, telling Texas reporters that his challenger was a "left-wing liberal Democrat" in the mold of Bernie Sanders.