SAN FRANCISCO — Gov. Jerry Brown’s push for a $6 billion annual tax increase faced high hurdles from the start: a long-standing antipathy to taxes among California voters; a rival tax plan by a multimillionaire civil rights lawyer and direct opposition from her equally wealthy brother; and even a last-minute, $11 million attack by a shadowy Arizona group whose backers remain unknown.

But voters resoundingly endorsed Mr. Brown’s ballot initiative by 54 percent to 46 percent on Tuesday, confounding most pollsters who had been predicting a closer outcome, if not outright defeat.

The victory was a big one for Mr. Brown, who, experts said Wednesday, had persuaded the state’s electorate to raise taxes for the first time since 2004 by shrewdly framing the plan as the only way to save California’s underfinanced public schools. Mr. Brown, a Democrat, had run for office after promising not to raise taxes without directly asking voters.