Galveston officials said 6,625 voters cast ballots in the city's runoff election.
Jaworski ended up with a little less than 3,000 votes, or 42.87 percent.
Also up for grabs was the City Council District 4 seat. Dianna Puccetti and Norman Pappous faced off Saturday.
Pappous defeated Puccetti with 460 votes, or 52.45 percent.