Across Texas, neither a red wave nor a blue one.

HOUSTON — The familiar contours of Texas politics held firm for another election despite a concerted effort and many millions in campaign spending aimed at proving otherwise.

As the votes came in on Tuesday, Democrats remained locked out of statewide offices — from the governor’s mansion to the agriculture commissioner’s office — and Republicans could point to some gains among Hispanic voters, winning an open congressional seat in South Texas, though fewer than they had hoped for.

The election did not feature dramatic shifts in either direction. “The RED WAVE did not happen,” said Representative Mayra Flores, a Republican who gained fame within the party by winning a special election in a Democratic district in the Rio Grande Valley this year only to lose on Tuesday.

Beto O’Rourke, the Democratic challenger to Gov. Greg Abbott, failed to attract enough new supporters to improve upon his performance in the U.S. Senate race in 2018, earning for himself a second statewide loss and renewed questions about his political future.

The surge of enthusiasm that lifted up Texas Democrats in 2018, creating a wave for many candidates at the local level, did not resurface. At the same time, the party avoided a complete wipeout in South Texas as incumbents in Congress — Representatives Henry Cuellar and Vicente Gonzalez — each won their races despite tough contests. (Mr. Gonzalez defeated Ms. Flores.)

Republicans managed to win back some voters in the suburbs, blunting what had seemed in recent elections to be promising inroads made by Democrats in these diversifying and fast-growing areas, particularly north of Dallas and Fort Worth.

Instead, those counties appeared to remain solidly in the Republican column, with Mr. Abbott carrying Collin and Denton Counties by wide margins. Tarrant County, which includes the city of Fort Worth and which Mr. O’Rourke narrowly won in 2018, also went for Mr. Abbott this time.

For the most part, Texas’ cities remained strongly Democratic, including the election to Congress of Greg Casar, a rising progressive star in a deeply blue district that includes Austin.

But an open question remained in Harris County, which includes Houston, where Republicans and conservatives spent heavily to unseat the Democratic county leader, Lina Hidalgo, another young and promising party leader.

The race was too close to call as of early Wednesday, and it was unclear whether the result would be affected by a legal fight over provisional ballots cast when polls stayed open an hour late, under a district court order, to make up for delays in opening at several locations. That order was blocked by the Texas Supreme Court, and the late-cast provisional ballots were segregated from the total.

The conservative sweep of statewide offices included Ken Paxton, the Trump-endorsed and criminally-indicted attorney general of the state, who was re-elected to a third term, and Dan Patrick, the hard-right lieutenant governor, who had drawn some opposition from his own party over his leadership of the State Senate, but not enough to make a difference in his re-election.

The victories appeared likely to result in a new round of conservative proposals when the Republican-dominated State Legislature meets next year. Among the topics discussed during the campaign were school vouchers, lowering the age for Texans to carry a handgun and a reduction in the burden of property taxes. Mr. Abbott has so far signaled resistance to adding exceptions to the state’s abortion ban for rape and incest.