AUSTIN, Texas - Tea party darling Ted Cruz convincingly defeated the Republican establishment favorite, Lt. Gov. David Dewhurst, in Texas' runoff election Tuesday, capturing the GOP nomination to replace retiring U.S. Sen. Kay Bailey Hutchison as fiercely conservative voters shook one of America's reddest states to its political core.

The race had been closely watched nationally as one of the most-vivid contrasts between the GOP mainstream and grass-roots, conservative activists. But as results began to pour in, it turned out to be no contest. Cruz completed the upset by grabbing advantages in key cities around the state where Dewhurst had once enjoyed stronger name recognition, fundraising and political organization.

"We are witnessing a great awakening," Cruz told cheering supporters in Houston shortly after Dewhurst called him to concede. "Millions of Texans, millions of Americans are rising up to reclaim our country, to defend liberty and to restore the Constitution."

More than 1 million Texans voted in the runoff, a surprisingly strong turnout for balloting that came during the dog days of summer.

"We're just tired of the government ignoring the Constitution," said Don Steinway, a 76-year-old retired commercial airline pilot who lives in Houston and described himself as a staunch supporter of the tea party.

Overseeing the state Senate from the powerful lieutenant governor's post since 2003, Dewhurst was long considered a slam dunk in his race with Cruz, the former state solicitor general and son of a Cuban immigrant.

Dewhurst had the endorsement of much of Texas' Republican mainstream, including Gov. Rick Perry, who despite his failed run for president is still widely popular back home. He also had a $200 million personal fortune he could dip into and did, loaning his Senate campaign at least $24.5 million.

But Cruz has a fiery stage presence that made tea party supporters across the state swoon, and received millions from national, conservative organizations that targeted Dewhurst as too moderate.

Even though the lieutenant governor oversaw some of the most-conservative state legislative sessions in Texas history and helped speed the passage of laws requiring women to undergo a sonogram before having an abortion and voters to show identification at the polls - he also occasionally compromised with Democratic lawmakers to keep the legislative agenda moving.

Looking exhausted and shaken, Dewhurst told a small crowd in another part of Houston, "We got beat up a little bit but we never gave up."

"We came up a little short this evening, which is something I'm not used to, being short," said Dewhurst, who stands well over 6 feet tall. "But we will never stop fighting for our beloved Texas."

Perry then released a statement calling Cruz "a force to be reckoned with: an excellent candidate and a great conservative communicator."

Meanwhile, former Democratic state Rep. Paul Sadler easily bested perennial candidate Grady Yarbrough to capture his party's nomination and face Cruz in November's general election, but Cruz begins that race the overwhelming favorite.

Sadler said that he stood "alone as the only nominee of a major political party in Texas because the Texas Republican Party has been hijacked by the tea party."

FreedomWorks organized volunteers for Cruz, and the group's president, Matt Kibbe, struck a similar tone but for a different reason, calling Cruz's victory: "the latest step in the American people's hostile takeover of Washington."

Cruz memorized the U.S. Constitution while in high school and successfully painted his opponent as wishy-washy - even though they actually disagree on little, either politically or ideologically. The 41-year-old Cruz had never run for political office but bolstered his political credentials arguing in front of the state Supreme Court as the longest-serving solicitor general in Texas history.

Texas Republicans aren't used to losing: The state has not elected a Democrat statewide since 1994. But Cruz attacked Dewhurst from the right, and the lieutenant governor's campaign had no real answer.

The state primary was pushed back from Super Tuesday to late May due to a legal fight over redistricting maps drawn by the GOP-dominated Legislature. The 66-year-old Dewhurst beat Cruz by 10 percentage points in the primary but fell about 70,000 votes short of the majority needed for an outright win in a nine-Republican field vying for the party's nomination.

But Cruz gained momentum just by surviving to force a runoff, and solidified his support in the race's final weeks. Things turned especially nasty in the late going, with both sides accusing the other of lying.

Dewhurst also was endorsed by former baseball great Nolan Ryan, as well as former Dallas Mayor Tom Leppert, who finished third in the Republican primary, and ex-NFL running back and ESPN commentator Craig James, the primary's fourth-place primary finisher.

None of it was enough.

Cruz was endorsed by ex-Alaska Gov. Sarah Palin, radio talk show host Glen Beck, U.S. Sens. Jim DeMint of South Carolina and Kentucky's Rand Paul, as well as former GOP presidential hopeful and Pennsylvania Sen. Rick Santorum.

"The message of this race couldn't be clearer for the political establishment: the Tea Party is alive and well and we will not settle for business as usual," Palin said via Facebook.

Natache Reeves, a 42-year-old nurse from the Dallas-Fort Worth suburb of Grapevine, said she voted for Cruz because he had Palin's support and was less likely to restrict handgun use.

"I love Sarah Palin, and she's backing Ted Cruz," Reeves said. "I pretty much agree with everything that rolls out of her mouth."

Cruz has drawn comparisons to Indiana, where state Treasurer Richard Mourdock defeated incumbent Sen. Richard Lugar in the Republican primary. But in Texas, the nation's second-most populous state, a win by a tea party-backed candidate is likely to resonate even more.

To Dewhurst's supporters, Cruz said, "We ask you to join us."

"We want you on our team," he continued. "In the heat of the campaign there have been harsh words spoken but I am hopeful that all of us can put them behind us and work together going forward."

Associated Press writers Juan A. Lozano and Ramit Plushnick-Masti in Houston contributed to this report.