Washington CNN  — 

Former Dallas County Sheriff Lupe Valdez won her runoff and became the Democratic nominee for Texas governor Tuesday night, making her the first openly lesbian and Latina nominee to win a major party gubernatorial nomination in the state.

Valdez won 53.1% of the vote while her competitor, Andrew White, obtained 46.9%, according to unofficial election results.

Valdez, a former US Army captain, accepted the nomination in a speech Tuesday evening, during which she advocated for equal opportunities for Texans.

“Tonight is a victory for all of us who are fighting for a stronger and fairer Texas. A tolerant and diverse Texas. A Texas where the everyday person has a voice and a fair shot – just as I had,” Valdez told supporters.

In a statement following her win, Valdez also said the victory “proved that no matter who you are, where you are from, or who you love – in this state, you’ve got a fighting chance.”

The former sheriff will face incumbent Republican Gov. Greg Abbott in the general election this November. Texas’ decades-long streak of support for GOP governors, along with Abbott’s incumbent status and $40 million-plus campaign war chest, make the general election a formidable challenge for Valdez, which she acknowledged.

“I am constantly hearing this is an uphill battle. Please – tell me when I didn’t have an uphill battle,” Valdez told supporters Tuesday night, later adding, “I am getting darn good at uphill battles.”

Valdez’s win came alongside a wave of Democratic women who dominated Tuesday’s primaries, including winning races in Kentucky and Texas and giving Georgia the first black woman to ever be nominated for governor by a major political party.

The victories underscored some emerging realities of 2018’s primary season: Female candidates – of which Democrats have record numbers in House races – have fared well. Political veterans’ experience, meanwhile, has been a burden. And while Democratic voters have valued candidates’ electability, the party’s base, energized by opportunities to put checks on President Donald Trump, has shown little interest in centrists.

CNN’s Eric Bradner contributed to this report.