Sanchez, who is the first Hispanic to win the nomination, had 59 percent, with 71 percent of the vote counted. Attorney General Dan Morales was trailing with 34 percent. Sanchez faces Republican Gov. Rick Perry, who had no primary opposition.
In his victory speech at Austin, Sanchez immediately launched his general election campaign against Perry to cheers of "Viva Tony, Viva Tony."
"It's time Texas has a governor that does more than rest on the laurels and accomplishments of his predecessor," he said, referring to Perry succeeding George W. Bush as governor. "Every Texan knows that for the past two years the governor's office has been vacant."
Sanchez said he would bring his experience as a "common-sense businessman" to the governor's office.
"I've met a payroll ... I've created jobs ... And I'll bring that experience to make Texas even better," he said. "That means a commitment to accountability in government, a belief that taxpayers call the shots, not the special interests that buy access, favors and vetoes."
In the Senate race, Victor Morales, the school teacher who challenged Sen. Phil Gramm in 1996, had 34 percent in the race for the Democratic Senate nomination, with 71 percent of the vote counted. Former Dallas Mayor Ron Kirk had 32 percent and Rep. Ken Bentsen 27 percent.
The top two candidates will face each other in an April 9 runoff, but late Tuesday night the outcome was still in doubt because of slow returns.
Attorney General John Cornyn was running away with the Republican Senate nomination with 77 percent, facing only political unknowns in his race.
Delays were expected in returns because a problem in San Antonio where voters were turned away from the polls because election judges were not in place.
State District Judge Michael Peden ordered the polls to stay open until 10 p.m. CST, three hours longer than scheduled, to accommodate turned-away voters.
Attorneys for several campaigns went to the judge after voters reported showing up at the polls and being turned away because election judges were absent.
Secretary of State Gwyn Shea predicted 5 to 10 percent of the state's 12.2 million registered voters would vote in the primary races.
The high-profile campaigns of the three Hispanic candidates may draw a record Latino turnout, according to Antonio Gonzalez, president of the William C. Velasquez Institute, a nonpartisan Latino public policy and research think tank.
"Latinos may be between 30 and 35 percent of votes cast on the Democratic side and that will be close to, if not, a new record," he said Monday "It would smash the record but I think some of the enthusiasm has been dampened by the negative campaigning."
Sanchez, a 59-year-old Laredo oilman, banker, and rancher, led Morales, a 45-year-old Harvard-educated lawyer, in the race for the Democratic gubernatorial nomination in recent polls.
In 11th-hour campaigning Monday, Morales accused Sanchez of buying the election. Sanchez had spent nearly $18 million in his campaign for the nomination, according to the latest spending reports. Morales had spent about $600,000.
Sanchez defended his spending, saying it was needed to make his name as well known as Morales, who was in public office for years as a prosecutor, legislator and attorney general.
"Dan Morales has been spending millions of dollars campaigning for 15 years," he said. "I've had to do in 20 months what he did in 15 years."
Sanchez will now face Perry, who would beat either Democratic candidate by a 2-to-1 margin, according to a recent poll by the Scripps Data Center.
Perry was in Sanchez's backyard Tuesday, signing an agreement with the governor of Nuevo Leon, Mexico to extend his proposed Trans Texas Corridor into the Mexican state. Perry said the corridor would ease the movement of people and goods between Texas and Mexico.
"By working together, we can connect Monterrey, Nuevo Leon -- the industrial heartland of Mexico -- to our Texas ports of entry all along the border. With new trade opportunities created by new trade corridors, we can continue to create good jobs and raise the standard of living for both of our peoples."
In the race for Democratic nomination to succeed retiring Republican Sen. Phil Gramm, a tight, three-way race was under way for weeks between Bentsen, Morales, and Kirk.
Bentsen, the nephew of former Texas Sen. Lloyd Bentsen, stressed his Washington experience, while Kirk, the first black mayor of Dallas, campaigned as a coalition builder. Morales, who draws name recognition from his 1996 campaign, ran a low-budget, populist campaign again.