In the Texas Congressional races, the first primaries are ahead of the upcoming battles.

And the newly formed, predominantly Republican district south of Houston will send Wesley Hunt, an Army veteran with West Point and Cornell degrees, to Congress, backed by Rep. Kevin McCarthy of California, the House Republican leader, who aspires to become Speaker. Mr. Hunt will strengthen the small but growing number of black members of the House of Representatives.

Representative Dan Crenshaw received three-quarters of the vote in his re-drawn constituency in suburban Houston despite far-right opposition. Mr. Crenshaw, an outspoken conservative, nonetheless brought in right-wing challenger Jameson Ellis after Mr. Crenshaw denounced the lie that the 2020 election was stolen from former President Donald Trump. Mr. Ellis attempted to call Mr. Crenshaw, a combat veteran who lost an eye in Afghanistan, “Republican in name only” or RINO, but garnered only about 15 percent of the vote.

In Texas’ Third District, just north of Dallas, Rep. Van Taylor remains at risk of being edged out by rivals on the right early Wednesday. These opponents criticized him for voting to create an independent commission to investigate the attack on the Capitol on January 6, 2021.

For Democrats, Ms. Cisneros’ victory will have real consequences.

Mr. Cuellar was perhaps the last remaining anti-abortion Democrat in the House of Representatives and ran to the right of his party on issues of immigration and border security. But instead of campaigning on the issues she ran in 2020, Ms. Cisneros revealed that after 17 years in Washington, the incumbent became corrupt and a prisoner of special interests, losing touch with the poor community she represented. Her story was reinforced in January when the FBI carried out a hitherto unexplained raid on Mr. Cuellar’s campaign headquarters and Laredo’s home.

The 28th district shocked both sides in 2020 when it turned sharply towards Mr. Trump. Hillary Clinton won heavily against Hispanic Zapata County in the county’s south, scoring over 30 points in 2016. It then went to Mr. Trump by about five points. Ms. Clinton’s 60-point lead in Starr County, which is 96 percent Hispanic, has narrowed to Joseph R. Biden Jr.’s five-point lead in 2020.

Ms. Cisneros said Trump’s hesitation was a sign that South Texas voters were open to an outside voice after so many years with Mr. Cuellar’s car. But with the young liberal as the Democratic nominee, the Republicans will undoubtedly play for the district in November.

The Republicans also faced a runoff to determine their flag bearer in the district, but Cassie Garcia, who received the most votes on Tuesday, was seen as one of the best candidates available to face Ms. Cisneros. She was Deputy State Director for Senator Ted Cruz, Republican of Texas, and Regional Representative for the Texas Agricultural Commissioner.

Jennifer Medina is reporting from Laredo, Texas.