Voters in this famously tax-averse state Tuesday night approved a temporary hike in the sales tax to stave off brutal budget cuts, handing Gov. Jan Brewer a crucial victory.

The veteran Republican had shocked many in her party last year by advocating the penny sales tax increase, arguing that the state couldn’t simply cut its way out of a deficit that rivals California’s. Critics said it was economic suicide to raise taxes in a recession.

On Tuesday night, as early returns showed two-thirds of voters agreeing with the governor, Brewer declared victory in front of supporters inside a middle school student union here.

“Arizonans have spoken today,” she said. “They told us our faith in them was well-placed.... They told us that doing the right thing almost always means doing the hard thing.”

Brewer’s advocacy of the tax increase divided the state GOP and turned politics upside down. At one point, the governor sued the Republican-controlled Legislature to force it to send her a budget. At last count, 20 challengers had signed up to face her in the August GOP primary.

She and the Legislature already had slashed $2 billion from last year’s budget and made Arizona the first to withdraw from a federal program to provide health insurance for children who live just above the poverty line. The housing collapse hit particularly hard here and took a huge chunk out of the state’s budget, which was $10 billion just two years ago but now hovers around $8 billion.

Proposition 100 mandates a temporary increase in the state sales tax — from 5.6% to 6.6% for three years. It’s expected to generate $1 billion per year.

Its apparent passage may have been aided by modest voter turnout, with only those who care deeply casting ballots.

But a leader of one of the groups that worked toward passage saw something more definitive in the results.

“This is Arizona treating education as an investment rather than an expense,” said Eileen Sigmund, the chief executive of Arizona Charter Schools Assn. “It’s a complete sea change. It’s people saying, ‘This is my state.’ ”

The measure was backed by many of the groups that Brewer infuriated by signing a controversial immigration bill, which requires Arizona police to determine the status of people they lawfully stop and suspect are in the country illegally.

Political observers have noted that because the governor was defying GOP orthodoxy by pushing the tax increase, she had little option but to sign the immigration bill, which is strongly supported by most Arizona voters and an overwhelming proportion of Republicans.

Public sector unions and many Democrats backed the tax initiative, as did several business groups. Taxpayer organizations and some small business groups opposed it.

Two voters typified the state’s drastic divide over the issue.

Carol Shaw, 60, a former Phoenix supermarket manager, opposed Brewer’s immigration stance but voted for the tax increase.

“Normally I’d be opposed to anything the governor’s for,” Shaw said. “This needs to happen; it’s long overdue. School kids need a break.”

But Darryl Blowers, 69, a retired accountant, voted no, saying he didn’t trust that politicians had cut as deeply as they said.

“They always lay out the worst-case scenario,” he said, “and that’s not always what happens.”

Earlier in the evening, before the results were known, Brewer spoke to reporters.

“Nobody likes taxes,” she said, recalling her shock at budget numbers when she took office in January 2009. “I pushed back and pushed back, but the more I looked at the figures from my economic people and my policy people, there was no other way.”

Rudy Espino, a political science professor at Arizona State University, said Brewer would have taken an immense political hit if the measure had failed. But now, he said, she can argue to primary voters that she was following popular sentiment.

“It’s harder to attack someone when they have a victory on hand,” he said.

nicholas.riccardi@latimes.com