Editor's note: This story has been updated throughout.

State Rep. Carol Alvarado, D-Houston, won a four-way special election to succeed former state Sen. Sylvia Garcia, narrowly avoiding a runoff against House colleague Ana Hernandez, according to unofficial results late Tuesday.

With all precincts reporting, Alvarado received 50.4 percent of the vote to 24.3 percent for Hernandez. Alvarado averted an overtime round by 59 votes out of 15,084 total.

Hernandez conceded shortly after all precincts came in, according to her campaign.

Republican Martha Fierro finished not far behind Hernandez with 23.2 percent. Her campaign refused to concede Tuesday night, claiming without evidence that there was voter fraud. But Lt. Gov. Dan Patrick, who presides over the Senate, congratulated Alvarado on her victory in a tweet, and the Texas GOP issued a statement accepting the outcome.

The fourth and final candidate, Democrat Mia Mundy, received 2.1 percent.

Alvarado is now poised to finish Garcia's term, which ends in January 2021, and her ascension to the upper chamber means there will be a special election to replace her in House District 145.

Garcia, a Houston Democrat, resigned last month after winning the race to replace retiring U.S. Rep. Gene Green, D-Houston. She initially sought an earlier special election for her seat, but that plan was derailed after a dispute with Gov. Greg Abbott over the validity of a July resignation letter.

In any case, Alvarado and Hernandez were ready for the vacancy in Senate District 6, which cuts across the eastern half of Houston and goes out to Baytown. Both announced their campaigns the day after Garcia won the March primary for Green's seat, all but guaranteeing a general-election victory in his deep-blue district.

It was Alvarado's second run for SD-6 after losing to Garcia in a 2013 special runoff for the seat.

The latest special election saw little open conflict between the two leading candidates, Alvarado and Hernandez. One notable exception was a debate where the two sparred over Alvarado's leadership roles in the GOP-dominated Texas House.