Dublin Mayor Tim Sbranti finished second with 17,270 votes, or 29.6% of the votes cast.
Two other Democrats in the race trailed, with Orinda Councilman Steve Glazer receiving 13,137 votes, or 22.5%, and Danville Councilman Newell Arnerich earning 6,651 votes, or 11.4%.
Baker and Sbranti will now compete in a runoff in the General Election Nov. 4.
Voting was light most of the day in Pleasanton as precinct workers often sat idle for lack of voters. The light vote was not a surprise in a mid-term congressional race and with no City Council or school board races on the primary ballot.
In the 15th Congressional District race, first-term Congressman Eric Swalwell (D-Dublin) held on to an early lead, garnering 28,292 votes, or 49.2% of all votes cast in that race, well ahead of challengers Hugh Bussell and State Sen. Ellen M. Corbett.
Bussell, the only Republican in the race, finished second with 25.9% or 14,901 votes, 610 more than Corbett who received 24.9% of the vote, according semi-officials results tabulated Wednesday morning.
Bussell, a Livermore resident and technology manager/educator, is vice chair of the Alameda County Republican Party and is employed by Workday in Pleasanton.
Under California's open primary format, the two candidates who emerged with the most votes, regardless of political party affiliation, move on to the November election, which means Swalwell, the Democrat from Dublin, and Bussell the Republican will face off again in November, if the second-place results hold.
State Sen. Mark DeSaulnier (D-Concord), whose senatorial district includes Pleasanton, will also find himself in a congressional runoff this November after earning 59.1% of the vote for the 11th Congressional District, which includes most of Contra Costa County extending north from Danville.
Retired Immigration Law Judge Tue Phan (R-Danville) will join DeSaulnier on the November ballot, placing second Tuesday with 27.8% of the vote.
In other races:
* Pleasanton school board member Jeff Bowser lost out in his bid to become Alameda County's new superintendent of schools. He finished third among the five candidates with 18,682 votes, or 17.89%.
Associate county superintendent Karen Monroe led the way with 35,536 votes, or 34.02% of the vote. San Lorenzo school board member Helen K. Foster finished second with 22,913 votes or 21.94%.
Since neither garnered more than 50% of the vote, Monroe and Foster will compete in a runoff for the position in November.
The other candidates were Ursula Reed, of San Leandro, with 14,436, or 13.82%, and Bay Area nonprofit executive Naomi Eason, who trailed with 12,254 votes, or 11.73%.
* Voters selected three incumbents and one challenger from seven candidates to serve on the Zone 7 Water Agency Board of Directors.
Sarah Palmer, a Zone 7 board director since 2006, led the ticket with 10,716 votes, or 21.10% of all votes cast in the election.
Other winners of board seats were challenger Jim McGrail, with 9,582 votes, or 18.86%; John James Greci, Jr. (in his 20th year on the board) with 8,594 votes, or 16.92%, and current board president Bill Stevens, with 7,019 votes, or 13.82%.
Incumbent AJ Machaevich failed to gain re-election, placing fifth with 6,090 votes. Challengers Alfred A. Exner (with 5,135 votes) and Matt Morrison (3,515 votes) finished sixth and seventh respectively.
* Pleasanton and Alameda County voters approved Measure AA, a countywide measure that extends until 2034 a half-cent sales tax that provides funds to help the county's public health system and for community medical services for low-income and uninsured residents.
With all votes counted, Measure AA received 94,865 Yes votes, or 74.50% of the votes cast for the measure, well over the two-thirds majority of votes needed to pass.
Votes against the measure totaled 32,474, or 25.50%.
* In a vote that could serve as a bellwether for advocates of a school parcel tax in Pleasanton, Livermore voters approved Measure G, extending a $138 annual school parcel tax.
The measure received more than the two-thirds favorable votes needed in that district's special election, with 71.18% Yes votes compared to 28.82% No votes.
The tax, which was first approved in 2004 and re-authorized in another vote in 2008, provides nearly $4 million in annual funding for Livermore schools.
* County voters elected Steve Manning as the new auditor-controller/clerk-recorder. The chief deputy auditor received 73.72% of the vote.
Businesswoman Kathleen Knox received 25.59% of the vote for auditor despite bowing out of the race late last month amid felony charges alleging she lied about living in San Leandro when actually residing in Danville. Knox, who pleaded not guilty to the counts, remained on the ballot because the removal deadline had passed.
* Four incumbents running unopposed won another term in their countywide posts: Sheriff-Coroner Gregory J. Ahern, District Attorney Nancy E. O'Malley, Treasurer-Tax Collector Donald R. White and Assessor Ron Thomsen.