Vasquez, who was elected to the board in 2002, garnered 4,087 votes, while Donald Pippo, who held the District 4 seat from 1983 to 1990, received 3,590 votes, unofficial election results show.
A candidate must obtain at least 50 percent-plus-one of the votes in order to avoid a runoff election.
The other two candidates, county employee Rebecca Benton and teacher's assistant Lisa Mullis, received 1,412 votes and 634 votes, respectively.
Solano County Sheriff Gary Stanton, who is serving his ninth year as sheriff-coroner, appears to have been re-elected with 39,557 votes against 664 write-in votes.
