Ted Cruz clinched the Republican nomination in the Texas Senate runoff race Tuesday night, handing the tea party a major victory and instantly becoming the odds-on favorite to win the open seat this fall.

Cruz, a Cuban-American lawyer who formerly served as state solicitor general, received 56 percent of the vote to 44 percent for Lt. Gov. David Dewhurst with 82 percent of precincts reporting.

"Tonight is a victory for the grass roots. It is a testament to Republican women, to tea party leaders and to grassroots conservatives," Cruz said in his victory speech. "This is how elections are supposed to be decided—by 'we the people.'"

Dewhurst, who was backed by Gov. Rick Perry, easily dominated the nine-candidate May 29 primary with 44 percent of the vote. But he failed to receive the majority required to avoid a runoff against second-place finisher Cruz. Due to significant tea party support and grassroots exposure, Cruz was able to stay competitive against Dewhurst, who remained well-funded and well-connected. As of July 11, Dewhurst had raised more than $24.5 million compared to Cruz's $9 million, according to reports filed with the Federal Election Commission.

At his concession speech, Dewhurst told an audience of supporters that this was not how he "envisioned" the night turning out. "We came up a little short this evening, which is something I'm not used to—being short," Dewhurst, who stands at 6-foot-5, said. "But we will never stop fighting for our beloved Texas."

Despite Dewhurst's electoral advantages, by the time of Tuesday's election, Cruz had become widely regarded as the runoff front-runner.

Cruz's victory is a major coup for the tea party, which had made this high-profile race a top target as it seeks to prove its continued electoral influence. Cruz drew support from Sarah Palin, Rick Santorum, Ron and Rand Paul, FreedomWorks, the Tea Party Express and many other groups and politicians for his underdog bid.

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"Ted Cruz is a champion of economic freedom and we look forward to seeing him fight for America in the Senate," Club for Growth president Chris Chocola said in a statement following Cruz's win. "Ted Cruz won because he clearly articulated the pro-growth message that Republican voters across the country have responded to. Tonight, Texas Republicans have shown Washington that the people do not work for the politicians—the politicians work for the people."

"This has been a hard-fought and spirited primary battle and the people of Texas would have been fortunate to have any one of these well-qualified candidates as their next U.S. Senator. But I could not be more pleased with the nomination of Ted Cruz and I offer my warmest congratulations to Ted, his wife Heidi and their two daughters," National Republican Senatorial Committee Chairman John Cornyn, a fellow Texan, said in a statement. "He and his team ran a remarkable race and this is a well-deserved and well-earned victory."

His win not only reinvigorates the tea party movement, it sends immediate shock waves through the Texas political establishment, which was firmly behind Dewhurst.

The tea party has scored major victories this cycle with the defeat of Indiana Sen. Dick Lugar and the victory of Wisconsin Gov. Scott Walker, who faced a recall vote. But some contests have proved to be losses, such as the Utah Senate primary.

Cruz this November will face former state Rep. Paul Sadler, who won the Democratic runoff Tuesday. The seat, currently held by retiring Republican Sen. Kay Bailey Hutchison, is favored to remain in Republican hands.