With Mr. Perry vacating his seat, the attorney general leaving his post to run for governor, the comptroller retiring and other offices being left up for grabs, this is the first time since 1998 that five of the six top statewide executive positions are open. If Mr. Dewhurst loses his bid for re-election — he will most likely find himself in a May runoff after the votes are counted Tuesday — it will be the first time in more than a century that all six jobs have new occupants, said Mark P. Jones, a political-science professor at Rice University.

Mr. Cruz’s victory has inspired other Texas Republicans to veer sharply right and to disregard the notion that they have to wait their turn for higher office. Mr. Delisi called it “the Cruz effect.”

“Texas politics has been defined by very careful, plodding and patient down-ballot officeholders,” said Mr. Delisi, a consultant to State Representative Dan Branch, a Republican who is running for attorney general. “Ted Cruz completely turned that on its ear. You can have a lawyer in his 40s upset the food chain and jump to a United States Senate seat.”

Nationally, the main focus on Texas has been the governor’s race, in which Attorney General Greg Abbott seems certain to face State Senator Wendy Davis as his Democratic opponent. But in Texas, most of the attention has been on the Republican primaries.

Candidates for state offices and the seat held by Texas’ senior senator, John Cornyn, who is being challenged by seven fellow Republicans, have appealed to the grass-roots conservatives and Tea Party activists who make up the bulk of the Republican primary electorate. Those appeals have steered the party from the center with tough talk of guns and God and of cracking down on abortion, illegal immigration, same-sex marriage and the Obama administration.

Image George P. Bush is running for land commissioner. Credit... Michael Stravato for The New York Times

The decision by Mr. Abbott to campaign with the rock musician Ted Nugent, who had earlier called Mr. Obama a “subhuman mongrel,” was seen by some as one of the dangers to mainstream Republicans of catering to the far right. Mr. Nugent reluctantly apologized for the words, but no Republicans suggested that he was an unacceptable face for the party.