Cooley, a Rancho Cordova city councilman, was elected with nearly 53 percent of the votes over Republican Peter Tateishi, formerly the chief of staff for Republican U.S. Rep. Dan Lungren.
Democratic candidates are leading in two other unresolved Assembly races. If they both prevail, Democrats will gain the 54 seats they need to control a two-thirds "supermajority" in the 80-member Assembly and be able to raise taxes without Republican votes.
In Orange County's 65th District, Sharon Quirk-Silva extended her lead over Republican Assemblyman Chris Norby to 1,701 votes with Friday's updated tally. There still are an unknown number of mail-in and provisional ballots to count.
Democrat Rudy Salas had a narrower lead in the Central Valley's 32nd District over Republican Pedro Rios. With more than 58,000 votes cast, Salas led by just 268. However, most of the remaining uncounted votes are in Kern County, which favors Salas.
Election officials said they planned to work through the weekend to count vote-by-mail and provisional ballots, though no new updates on vote totals were expected until Monday.
Democrats already won a Senate supermajority in Tuesday's elections, even with two still-unresolved races. If they add the Assembly, it will be the first time since 1883 that they will have such overwhelming majorities in both chambers. Republicans last had such advantages in 1933.
In one race, Democratic Assemblywoman Cathleen Galgiani trailed Republican Assemblyman Bill Berryhill by about 4,800 votes in the Central Valley's 5th Senate District.
And in a special election to fill the 4th District seat, Republican Jim Nielsen had a huge lead over Democrat Michael Harrington in the six-candidate race. However, to avoid a runoff he must get a majority of all votes and with thousands still uncounted it was unclear whether he would. Through Friday, his vote total was 50.4 percent.