The survey, by the Public Policy Institute of California, found that 52% of likely voters back Brown in the November election, while 33% support Kashkari.
Both candidates have strong backing from their respective parties -- 80% of Democrats support Brown, while 70% of Republicans say they'll vote for Kashkari. But Brown also has the advantage among independent voters: 52% of independents back the incumbent governor and 28% support Kashkari.
The poll, which focuses on environmental policy, found that 68% of Californians support AB 32, the 2006 climate change law that requires the state to reduce its greenhouse gas emissions.
Around three-quarters of Californians support a provision of the law that, starting next year, would apply the cap-and-trade rules to motor vehicle fuels. But that support plummets to 39% if that results in higher gas prices, as some opponents contend it would. A bill currently making its way through the Legislature would postpone including transportation fuels in the cap-and-trade system until 2018.
Similarly, 76% of those polled back a 2011 state law that calls for one-third of the state's electricity to come from renewable energy by 2020, but that support drops to 46% if that results in higher electricity costs.
"Californians want to see government action to reduce greenhouse gas emissions, but their strong support for clean energy policies diminishes if they have to pay higher electricity bills or gas prices," said Mark Baldassare, PPIC's president.
Respondents also expressed wariness over hydraulic fracturing, or "fracking," the controversial oil and gas extraction method, with 54% of adults saying they opposed more fracking in the state.
Thirty-five percent of Californians said
The poll found a slim majority -- 51% of likely voters -- in support of the $11.1-billion water bond currently on the November ballot. That support grows to 59% of likely voters if the bond's price tag was lower. Legislators have been trying to negotiate a pared-down measure to replace the current bond, which was written in 2009.