Reynolds received 125 votes while his opponent, Sharon Chesser received 109 votes. Reynolds will face Republican candidate Brenda Hansler in the Nov. 4 general election.
Moy received a total of 2,057 votes across the five-county district while her opponent, Sylvia Rodriguez received 1,610 votes.
A total of 240 votes were cast for Moy in Atascosa County, 601 in Frio County, 606 in Karnes County, 215 in La Salle County and 395 in Wilson County.
A total of 104 votes were cast for Rodriguez in Atascosa County, 620 in Frio County, 164 in Karnes County, 307 in La Salle County and 415 in Wilson County.
Moy will face Republican candidate Russell Wilson in the Nov. 4 general election. Wilson ran unopposed in the Republican primary election.
For detailed statewide runoff results, visit www.sos.state.tx.us.