Cole will face off against Gabriel Nila in November's general election after Nila ran unopposed for his party's nomination.
Elsewhere, Maya Guerra Gamble defeated Aurora Martinez Jones in the Democratic district judge race for the 459th Judicial District, and Julie Oliver earned the U.S. House District 25 Democratic nomination in a close victory over Chris Perri.
In Tuesday night's local Republican primary races, Chip Roy will earn the party's U.S. House District 21 nomination, and Mike Toth defeated Donna Davidson for a nomination to the 3rd Court of Appeals.
Turnout was up in Travis County in 2018 from the 2014 and primary runoffs, reaching 8.51 percent, which could likely be attributed to governor and U.S. House races on the ballot.
You can find Tuesday night's full local results here.