WASHINGTON - Two years after Ted Cruz upset the political establishment in the Lone Star state by winning election to the Senate, Texas voters helped two major Republican establishment candidates in marquee races secure their posts in the state's primaries today.

Sen. John Cornyn, the second highest ranking Republican in the Senate, crushed his primary opponents with well over the 50 percent of the vote needed to avoid a run-off May 27. The Associated Press called the race for Cornyn, who is seeking his third term in the U.S. Senate, shortly after polls closed tonight.

Cornyn's closest challenger was Rep. Steve Stockman, who gave up his House seat to run against the two-term senator. Stockman, a well known tea party firebrand, entered the race on the day of the filing deadline but quickly disappointed many conservative activists hoping to uproot Cornyn from his Senate office.

In another establishment vs. tea party test, Rep. Pete Sessions, chairman of the House Rules Committee, beat his tea party opponent Katrina Pierson in the primary for his seat representing Texas' 32nd Congressional district. Tea party activists had their eye on the Sessions race as a potential upset, but Pierson's candidacy fizzled out despite endorsements from Sarah Palin and Rafael Cruz, the father of Senator Cruz.

The success of Cornyn and Sessions in Texas could offer hope to other establishment candidates across the country in 2014. The mid-term election is teeming with establishment vs. tea party matchups - from the Republican primary in the Kentucky Senate race between Senate Minority Leader Mitch McConnell and tea partier Matt Bevin, to the Mississippi primary race between Sen. Thad Cochran, who is seeking a seventh term, and tea party favorite Chris McDaniel.

The primary results come as a new ABC News/Washington Post poll released Tuesday found that 47 percent of Republicans and Republican-leaning independents called it a bad thing for tea party candidates to challenge Republican incumbents.

But the tea party did see success in other statewide contests: the Republican primary for lieutenant governor. State Sen. Dan Patrick, a conservative radio host from Houston, secured more votes than current Lieutenant Governor David Dewhurst, but did not clear the 50 percent threshold needed to avoid a run-off. Dewhurst, who has served as lieutenant governor for more than years, was already politically wounded after losing to Cruz in the Republican run-off for the Texas Senate race in 2012.

The attorney general's race will also head to a run off between state Rep. Dan Branch, a well-funded establishment candidate, and state Sen. Ken Paxton, a Tea Party favorite it led in the polls, but failed to secure the 50 percent to avoid a run-off.

The oldest member of Congress will also face a run-off later this spring. At age 90, Rep. Ralph Hall failed to receive the 50 percent needed to secure his party's nomination for his seat in Texas' 4th Congressional district, which he's held since 1981. Ralph will face John Ratcliffe, a 48-year-old former U.S. attorney, in the May run-off.

Hall recently tried to combat charges that he is too old for elected office with an ad playfully highlighting the wrinkles on his face he said he acquired after fighting against liberals.

Gubernatorial candidates Attorney General Greg Abbott and state Sen. Wendy Davis easily coasted to win their respective party's nominations, as did George P. Bush, who is running for Texas Land Commissioner and is the newest Bush family member to seek political office.