Sekula Gibbs had 30 percent of the vote to Olson's 21 percent with nearly all precincts reporting.
"Our campaign team is really eager to go forward to continue the hard work and sacrifice and begin the process of healing and bringing all Republicans together so we can have a unified, conservative voice so we can win this seat back in November," Sekula Gibbs said.
Republicans have made incumbent Democrat Nick Lampson of Stafford their No. 1 target in this year's elections. Sekula Gibbs failed to beat Lampson as a write-in candidate in 2006. But she won a special election as a temporary replacement for DeLay in Congress and served for two months after investigations forced DeLay to resign.
She carries some baggage into the race. A day after she was sworn in to replace DeLay, staffers walked out in protest of her accusations they were deleting files. The staffers were cleared of any wrongdoing.
She also drew some derision when she told reporters she planned to resolve such thorny issues as tax cuts, immigration reform and the Iraq war in less than three weeks.
Olson served as chief of staff to Texas Republican Sen. John Cornyn from 2002 to 2007 and was an aide to former Sen. Phil Gramm, also a Texas Republican. He has been emphasizing his Naval aviator career in his campaign.
All the state's 32 U.S. House seats were up for re-election Tuesday night. Republican Rep. Ron Paul essentially sealed his re-election to Congress after his primary victory. But his presidential tally was only 5 percent in his home state, despite being an Internet sensation.
"I have a free ride now for a while. I don't have a Democratic opponent. The district is pretty safe for me so I can deal with district and national problems," Paul said.
In District 23, former Bexar County Commissioner Lyle Larson won the Republican nomination to challenge Democratic Rep. Ciro Rodriguez. They'll contend for the largest district in Texas, which stretches from San Antonio to the U.S.-Mexico border and west toward El Paso.
Rodriguez won it two years ago after the Supreme Court rejected the 2003 GOP redistricting that subbed 100,000 white voters for Hispanic voters. The growth of Hispanic voters in the district and increase Democratic turnout could factor into the race.
Among Democrats, Larry Joe Doherty, who played a judge on TV's "Texas Justice," heads to a matchup with District 10 incumbent Rep. Mike McCaul of Austin. Doherty had 60 percent of the vote with most precincts counted. Doherty predicted tough fundraising because of McCaul's personal wealth.
Incumbent Rep. Sam Johnson will seek his 10th term against Democrat Tom Daley.
Other incumbent winners were Reps. Ralph Hall, R-Rockwall and Silvestre Reyes, the House Intelligence Committee chairman. Hall, who is 84, is pitted against Democrat Glenn Melancon and Reyes, D-El Paso, is unchallenged in November.
Democrat Dwight Fullingim will face incumbent Rep. Randy Neugebauer, R-Lubbock. Republican John Faulk takes on Democratic Rep. Sheila Jackson Lee of Houston.
Democrats Steve Love and Eric Roberson advanced to a runoff for the Dallas District 32 seat held by Republican Rep. Pete Sessions.
In the Senate, incumbent John Cornyn defeated Larry Kilgore for the Republican nomination. Democrat Rep. Rick Noriega led in the Democratic primary.
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