The Senate's second-ranking Republican defeated a slate of primary challengers Tuesday, winning his party's nomination outright and taking a big step toward securing a third term in the upper chamber.

Sen. John Cornyn (R-Tex.) (Andrew Harrer/Bloomberg)

Sen. John Cornyn (R-Tex.) defeated Rep. Steve Stockman (R) and six other gadfly Republican candidates, carrying 61 percent of the vote according to early returns. The Associated Press called the race for Cornyn just minutes after all polls closed in the state.

Stockman, a congressman with a knack for stoking controversy, entered the race at the eleventh hour. His campaign gained no traction and he failed to unite tea party groups behind his cause. Conservative activists grumbled about Cornyn's record throughout 2013. But they came to terms late last year with the fact that a serious challenger was not going to step up to take him on.

Half the Republican senators running for reelection this year face contested primaries. Cornyn prepared for a threat early, hiring a tea party activist as his campaign manager and taking nothing for granted, having learned from the failures of Richard G. Lugar and Robert Bennett, two senators who failed to respond to the tea party threat soon enough during the past couple of election cycles.

Cornyn will begin the general election as a commanding front-runner. Democrats faced a new headache when dentist David Alameel was forced to endure a May runoff against Kesha Rogers, a Lyndon LaRouche acolyte who has called for President Obama's impeachment.

"During the General Election campaign we will cede no voter and no region of Texas," Cornyn said in a statement. "To keep Texas on the right track and save our country we must be a welcoming party to all who share our principles and values."

A trio of other congressional primaries was under the spotlight Tuesday night. Rep. Ralph Hall (R), the oldest sitting member of Congress, was forced into a runoff in the 4th district. He will face former U.S. Attorney John Ratcliffe.

In the 23rd, a sprawling district in southwestern Texas, former congressman Francisco "Quico" Canseco (R) is vying for a rematch against Rep. Pete Gallego (D), who defeated him in 2012. But Canseco was forced into a runoff against former CIA officer Will Hurd (R). Meanwhile, Rep. Pete Sessions (R) easily defeated a challenger who was backed by FreedomWorks, a national tea party group.

In the open governor's race, Attorney General Greg Abbott (R) and state Sen. Wendy Davis (D) cruised to a general election match-up that Abbott will begin as a substantial favorite to win, thanks to the state's strong conservative tilt. Davis rose to national fame last year when she filibustered antiabortion legislation for 11 hours. She's raised a lot of money so far, enabling her to compete in the state's many expensive media markets. But Texas hasn't elected a Democrat to a statewide post in 20 years and Abbott is well-liked by Republicans.

Down the ballot in other statewide races, tea party candidates had more success against establishment Republicans than they did in federal races. Lt. Gov. David Dewhurst (R) was headed for a second place finish and runoff against state Sen. Dan Patrick (R), a conservative radio host running to his right. Meanwhile, state Sen. Ken Paxton, a conservative emulating Sen. Ted Cruz (R-Tex.), advanced to a runoff against state Rep. Dan Branch in the race for attorney general.

In another closely watched contest, Bush family scion George P. Bush (R) took a step closer to becoming land commissioner, a powerful statewide position. The nephew of former president George W. Bush and son of former Florida governor Jeb Bush (R) was leading his only Republican opponent by a wide margin. Bush is the frontrunner in the general election.

George P. Bush, son of former Florida governor Jeb Bush, wins the Republican nomination for Texas land commissioner. (Reuters)

This posted has been updated with fresh results