Alvarado took 50.4 percent of the vote in Tuesday's special election to Hernandez's 24.3 percent in the Democrat-friendly district. She will complete Garcia's term, which ends in 2021.
Republican Martha Elena Fierro took 23.2 percent of the vote, while Democrat Mia Mundy took 2.1 percent.
Last month, Garcia won a Houston-based U.S. House seat being vacated by long-serving Democrat Gene Green.
In January, she and El Paso's Veronica Escobar will become the first Hispanic women to represent Texas in Congress.