Quintero received 36 percent of the vote.
Elorduy, 60, said in his victory speech his party has a great responsibility.
"Mine will be an ‘adding' government," said a tearful Elorduy as he invited those from all government parties to have a role in his administration.
Quintero said during a press conference that "the official results are not available, and the only information we have is an exit poll broadcasted on a television station."
That exit poll stated Elorduy was the winner of the election.
Alberto Reza-Saldaña, PRI state president, said, "We will wait to hear the official results on Wednesday."
The PRI leader said there were too many ‘abnormalities' in the election.
Outgoing Mexicali Mayor Víctor Hermosillo and Víctor Beltrán Corona, president of the electoral council, said "minor" incidents occurred during the election.
Hermosillo said some polling sites opened late, but, he said, he knew of no other problems.
PRI representatives blamed outgoing state Gov. González Alcocer, a PAN member, for conducting a campaign meant to favor the PAN candidate.
It is illegal for any government official to campaign in support of candidates at the federal, state and local levels.
At the Crowne Plaza Hotel, where the PAN had its press room, Elorduy said, "If God wants, we will make the best government Baja California has ever had."
Other election results from Mexico show that PAN has won at least four of the five mayoral races in Baja California, and at least 13 of 16 assembly seats in the Chamber of Deputies.
Ochoa said he looks forward to serving as mayor of Mexicali. He said he will work very close with "his neighbors" of Imperial Valley.
He said in an interview after he voted, issues like pollution, public security and regional industrialization are the most relevant matters to both sides of the border.
Francisco Garcia Burgos, state PAN president, said, "There are other issues in which we have to work on, but I know Eugenio Elorduy will do well to solve problems with the California government."
As PAN members were celebrating the party's triumph over PRI, others were more worried about the low voter turnout.
"We did everything that was possible to make citizens go out to vote," said Beltrán Corona, electoral institute president.
Preliminary results show that more than 500,000 registered voters cast ballots out of 1.5 million registered voters in the state.
Luis Felipe Bravo Mena, national PAN president, when asked by a reporter if Elorduy's government will be a government of the minority, said, "He won with the majority of votes, and that is the only relevant issue."
Reports from Tijuana on Sunday, stated Mexican citizens were lining up at the port to drive into San Diego rather than vote.
"All who don't care about their families and their community are committing a moral fault," said José Isidro Guerrero, Mexicali Catholic bishop, interviewed after he voted at the same polling place as Elorduy.
Socorro Lizárraga, who lives in rural Mexicali, and got surgery three days ago, was treated in Mexicali and was cared for by her family.
She couldn't get back to her community in rural Mexicali and wasn't allowed to vote at a special polling place located in the south section of Mexicali because it was not her designated polling site.
"They (the authorities) said there were going to be special sites where one could vote if we were out of our places, and this is pretty bad for us," she said.
Also, police reports stated some voters in the poor neighborhood of Solidaridad in the outskirts of Mexicali were not allowed to vote, reportedly because their names were not on the approved list of voters.
"We will check this out," Corona said.
Staff Writer Arturo Bojorquez can be reached at 337-3451.