Updated at 10:53 p.m. ET: Tea Party-backed Ted Cruz won the primary runoff contest for the Texas Senate seat Tuesday night with over half of the vote, beating Lt. Gov. David Dewhurst, who was the winner of a plurality of the vote in the initial primary election in June. Dewhurst conceded Tuesday night.

Cruz will face Rep. Paul Sadler in the general election, which will determine the successor to retiring Sen. Kay Bailey Hutchison (R). Sadler beat former educator Grady Yarbrough in Tuesday's primary with two-thirds of the vote.

But given the Republican dominance in Texas, the seat is seen as likely to remain in GOP control, which made Tuesday’s runoff a somewhat de facto general election.

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The Dewhurst-Cruz battle marked another chapter in the battle between the establishment and insurgent wings of the Republican Party, splitting Republicans along familiar dividing lines.

Dewhurst had been able to outraise his primary opponents in part thanks to his long time in government and his support from Texas Gov. Rick Perry (R), whose highly-regarded staff had managed his campaign.

But after Dewhurst failed to win an outright majority in the June 2 primary – which would have secured for him the nomination – conservatives who had opposed the lieutenant governor rallied around Cruz as the conservative alternative in the primary runoff.

Familiar Republican figures who had propelled other upstart conservatives in primaries had rallied around Cruz. South Carolina Sen. Jim DeMint endorsed the former solicitor general, and former Alaska Gov. Sarah Palin and former GOP presidential candidate Rick Santorum each stumped for Cruz last weekend in Texas.

Cruz, a Cuban-American who had served as a onetime clerk to the late Chief Justice William Rehnquist, had been the favorite going into the primary on Tuesday. But Dewhurst supporters held out hope that early voting might carry the day for his campaign.

Texas seems likely to have a more conservative senator in Washington come next January. The outgoing Hutchison is regarded as a generally Republican, but had drawn conservatives’ ire for supporting abortion rights and the 2008 Wall Street bailout program.