Former Dallas Mayor Tom Leppert was a distant third with 13 percent of the vote, while six other candidates had less than 4 percent.
The results were as expected in a race — the latest contest this year featuring “insurgent” conservatives challenging establishment Republicans — that had grown increasingly nasty and expensive in recent months.
Mr. Dewhurst, 66, a rancher and businessman with an estimated net worth of $200 million, has the backing of state GOP leaders, including Gov. Rick Perry. Mr. Cruz, 41, who has embraced the tea party mantle, has been endorsed by former Republican vice-presidential nominee Sarah Palin and by a group of conservative GOP senators.
Mr. Dewhurst has touted his experience in the Air Force, the CIA and in business, as well as a statewide political career that began in 1999 as the commissioner of the Texas General Land Office.
Democrats also picked a Senate nominee Tuesday, with Paul Sadler holding an almost 10-point lead over his nearest rival in a four-way primary race with 53 percent of the precincts counted.
But the Democratic Party’s candidate is likely to be an overwhelming underdog come November.
Political experts say it’s too early to tell who would have the advantage in a Republican runoff, as much depends on whom the seven also-ran candidates would support. And with the intraparty battle extended for two months, more outside money may flood into — and influence — the race.
Turnout was light in a state where GOP primaries in recent years have attracted turnouts of less than 5 percent of the eligible voting population.
In other Texas races, Randy Weber held a 9-percentage point lead over his nearest competitor in a nine-candidate GOP scramble to replace the retiring Rep. Ron Paul.
Nine-term Democratic Rep. Lloyd Doggett was declared the winner in a three-way race in a newly-created San Antonio-area district after crushing his nearest opponent by 47 points.
The district is one of four new congressional districts awarded to Texas because of its surging population growth the past decade.
Mr. Dewhurst saw a comfortable double-digit poll lead shrink in recent months. Results of a University of Texas/Texas Tribune survey released last week showed the lieutenant governor with a 9-point advantage over Mr. Cruz.
Both campaigns viciously attacked the other.
The Dewhurst campaign accused Mr. Cruz of being the lead attorney for a Chinese manufacturer charged with stealing the intellectual property of an American businessman. Mr. Cruz disputes that he is the primary counsel in the case.
Mr. Dewhurst in recent days stirred up another controversy, accusing Mr. Cruz of supporting amnesty for illegal immigrants because of affiliations with two groups the Dewhurst campaign says back amnesty. Mr. Cruz has denied the charge and pushed back, accusing his rival of not doing enough to secure Texas’ border with Mexico while serving as lieutenant governor.
The contest has already become one of the most expensive primaries in history, attracting more than $6 million from outside groups, according to OpenSecrets.org, a nonpartisan website that tracks money in politics.
Mitt Romney was declared the winner in the Texas GOP presidential primary, securing the additional delegates he needed to clinch his party’s nomination in Tampa, Fla., in late August.