The second- and third-place finishers were fewer than 900 votes apart in the unofficial tally, though, and Republican Eric Roach considered that too close to call.
The winner of the June 6 runoff will serve the remaining eight months of Cunningham's term. Cunningham, a longtime Republican congressman who was convicted of tax evasion and bribing defense contractors, will be in federal prison.
"People know that this district today voted for change in Washington," election winner Francine Busby told supporters Tuesday night. "We sent a message that we will no longer accept business as usual."
Busby, who was trounced by Cunningham at the polls two years ago, topped an 18-candidate field Tuesday in the wealthy, heavily Republican Southern California district, but she didn't get the 50 percent of the vote necessary to prevent a runoff.
With 100 percent of the precincts reporting early Wednesday, Busby had 56,147 votes, or 44 percent. Bilbray had 19,366 votes, or 15 percent, followed by Roach, a political newcomer who spent $1.8 million on his own campaign, who had 18,486 votes, or 14 percent, according to unofficial results.
Late Tuesday, after 99 percent of precincts had reported, Roach spokesman Stan Devereux said the election was too close to call. "It may be another day or two until we know what the outcome is," he said.
Bilbray, however, seemed confident of victory, saying his campaign against Busby would begin Wednesday.
Cunningham had represented the district from 1993 until he resigned in disgrace late last year. In March, he was sentenced to more than eight years in federal prison on charges of evading taxes and accepting $2.4 million in bribes from defense contractors.
Turnout appeared light at the polls. Volunteers at a polling place in San Diego's Del Mar Heights neighborhood reported only 16 people had voted by lunchtime, and voters were scarce at a sampling of polling places.
John Towers, a 51-year-old Republican who voted for Roach, said he felt betrayed not only by Cunningham, but by the policies of the Bush administration.
"I wouldn't be surprised if a lot of Republicans are so disgusted they just stay home," said Towers, of Cardiff.
Also Tuesday, political newcomer Barbara Ann Radnofsky defeated perennial candidate Gene Kelly for the Democrats' U.S. Senate nomination in the most high-profile of Texas runoff races.
Radnofsky, a Houston attorney, had 123,745 votes, or 60 percent, compared with Kelly's 83,340, or 40 percent, with 99 percent of precincts reporting, according to unofficial returns. Radnofsky will now face Republican Sen. Kay Bailey Hutchison in November in what will be a long-shot attempt to unseat the entrenched incumbent.
"Just as aging prom queens need to get out of the way and move over for the new crop, the new blood, I think it is time for her to move on," Radnofsky said.
Hutchison issued a brief statement, saying if re-elected she "will continue to be a senator for all Texans."