Whitman spent more than $70 million of her money in her campaign to succeed Schwarzenegger, a moderate Republican.
In a bid to win over conservatives, Poizner made immigration the defining issue of his campaign, supporting the controversial Arizona law on illegal immigration and attacking Whitman for opposing it.
Whitman will face Democrat Jerry Brown, the state's attorney general, in the fall. Brown previously served as governor from 1975 to 1983.
Today's primaries could be the last to be held in the state.
A ballot initiative seeks to limit the general election to two members of the same party.
Proposition 14 would replace party primaries with a "top-two" election structure for congressional, statewide and state legislative elections. All candidates would be included in a single primary election open to all voters, regardless of party registration. Candidates would have the option to declare a party preference or appear on the ballot with no affiliation.
The two candidates with the highest vote totals in the primary would then advance to a general election. Write-in votes would be ignored. The November ballot thus could feature two members of the same party as the only options.
ABC News' David Chalian, Devin Dwyer, Alex Pepper and Jonathan Karl contributed to this report.