The race between the two main Republicans vying to challenge Gov.
The Democratic incumbent remains a strong favorite in the June 3 primary, according to the Public Policy Institute of California poll.
The survey found 48% of likely voters backing Brown, followed by 15% for Donnelly and 10% for Kashkari. The candidates who finish first and second, regardless of party, will compete in the November election.
Donnelly's lead over Kashkari falls within the poll of likely voters' margin of error of 4.9 percentage points in either direction.
While both GOP candidates have gained support in recent weeks, roughly a third of Republicans remain undecided, according to the survey. That portends a hard-fought contest in the campaign's 12 final days.
Donnelly, who lives near Lake Arrowhead, is a former leader of the Minuteman volunteer border patrol group who was first elected to the Assembly in 2010. Kashkari, who administered the federal bank bailout and now lives in Laguna Beach, is making his first run for public office.
In April, a poll by the institute found Donnelly was the top Republican, with 9%, and Kashkari barely registering, with 2%.
The new survey underscored Brown's strong position in his bid for an historic fourth term. It found 54% of likely voters approved of the way he was handling his job and 35% disapproved. Even among Republicans, 27% gave Brown a positive job rating, and 62% approved of his most recent budget plan.
As for the Legislature, the poll found that the criminal prosecution of three state senators has had little effect on public opinion. Just over two-thirds of the adults surveyed said the state was pretty much run by a few big interests looking out for themselves, roughly the same finding as in December before the three senators were suspended.
"Distrust in government runs high among Californians," said Mark Baldassare, the institute's president and chief executive.
On other issues, the poll found strong majorities of Californians said they had cut back on water use at a time of severe drought. And 54% opposed the expansion of fracking, the controversial oil and gas extraction method that Kashkari and Donnelly have championed.