New Jersey Gov. Chris Christie won a decisive reelection victory on Tuesday, as the Republican known for blunt talk, moderate politics and presidential ambitions won support from a wide swath of voters in his Democratic-leaning state.

Christie, running for his second term, was leading state Sen. Barbara Buono (D) by more than 20 percentage points late Tuesday with more than 98 percent of precincts reporting. His victory was a hopeful sign for the GOP’s establishment wing, on a day when two champions of the party’s rival tea party faction lost their races: gubernatorial candidate Ken Cuccinelli II in Virginia and House hopeful Dean Young in Alabama.

“A dispirited America, angry with their dysfunctional government in Washington, looks to New Jersey to say . . . ‘Are people really coming together?’ ” Christie said in his victory speech in the town of Asbury Park. He said that New Jersey could be a model for Americans working together.

“Maybe the folks in Washington, D.C., should tune in their TVs right now, see how it’s done,” he added.

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Chris Christie logged one for the record books when he was reelected governor of New Jersey Tuesday night. (The Washington Post)

Elsewhere on Tuesday, New York City elected a Democratic mayor, Bill de Blasio, for the first time since 1989. Voters in Detroit chose the city’s first white mayor in nearly 40 years. Voters in Colorado rejected a ballot measure that would have raised large amounts of money for education, and approved a measure to tax marijuana.

The marquee elections on Tuesday were the two gubernatorial contests, which provided a look at two faces of the modern GOP. In Virginia, Cuccinelli — the state attorney general who rose to prominence because of his strong views on social issues and his strident opposition to President Obama’s policies — stood for the take-no-prisoners wing. But those stances provided fodder for Democrats, who hammered Cuccinelli’s socially conservative views on women’s issues. Public opinion polls taken in the late stages of the race showed Cuccinelli suffered as a result.

In New Jersey, Christie has come to embody a more pragmatic brand of Republican governance — although not necessarily a gentler one, as a recent shouting match with a critic showed.

Christie publicly lambasted House Republicans in January for not acting on a bill that would provide Hurricane Sandy relief and moved even further away from Washington last month when he declared that “ ‘compromise’ isn’t a dirty word” in a campaign ad released the day lawmakers forced a federal government shutdown.

In his state, Christie was praised for his response to the hurricane last fall, including his post-storm appearances with Obama. The governor’s image has soared in the Garden State this year, leaving Buono struggling to slow his march toward a second term.

“The glow of Sandy hasn’t worn off nearly as much as Buono hoped,” said Ben Dworkin, a political scientist at Rider University. “The governor had an approval rating north of 60 percent just days before the election.”

Christie appeared on course to win more than 50 percent of the vote statewide, the first time a Republican had done that in deep-blue New Jersey since George H.W. Bush in the 1988 presidential election.

Exit polls showed that Christie did better with many groups of voters than he had in 2009. They showed he had won 57 percent of female voters, up 12 percentage points from his first election. He won 21 percent of African American voters, which also was up 12 points. Christie won 51 percent of the Hispanic vote, which was up 19 points.

The governor also improved his showing among the group that can be hardest for Republicans to win over: Democrats. Exit polls showed 32 percent of Democrats supported him, which was up 24 points from 2009.

But, for Christie, the clash that’s coming with the GOP’s hard-right faction is probably still a couple of years and a number of states away. It won’t be settled, perhaps, until the early nominating contests in New Hampshire and Iowa in 2016.

In Alabama on Tuesday, there was a preview of the same fight. In a GOP runoff in the state’s 1st Congressional District, business-backed Bradley Byrne beat Dean Young — a Christian conservative aligned with the tea party movement — by about five percentage points.

A Byrne win is a boon to business-minded Republicans keen on electing candidates less likely to push the country toward more economic showdowns. Byrne said he doesn’t think shutting down the government was a good thing, while Young said it “was not the end of the world.”

The U.S. Chamber of Commerce spent at least $199,000 to help Byrne. Donors to his campaign include big corporations such as AT&T and Aflac.

In New York City, meanwhile, the liberal de Blasio steamrolled his Republican opponent, holding a lead greater than 40 points. That was the end of a remarkable turnaround for him. The onetime underdog in the Democratic race catapulted into the lead as higher-profile candidates such as City Council Speaker Christine Quinn and former congressman Anthony Weiner foundered. He never looked back. De Blasio’s Republican opponent, Joe Lhota, lagged well behind in polls throughout the fall campaign.

It is also a remarkable political turnabout for the city. A former councilman who served as the city’s public advocate, de Blasio has been a harsh critic of ­Michael R. Bloomberg, the city’s outgoing Republican-turned-independent mayor, accusing him of being out of touch with the city’s working-class and poor residents.

In Detroit, Mike Duggan was elected the city’s first white mayor in four decades. The former hospital executive — who sold himself as a change agent — faces deep challenges in a city battered by persistent economic decline, civic corruption and municipal bankruptcy.

In Boston, voters chose Democratic state Rep. Martin Walsh to replace retiring Democrat Thomas Menino, the city’s longest-serving mayor.

Ballot initiatives in a handful of states were also in the spotlight Tuesday. Colorado voters approved a new 25 percent sales and excise tax on marijuana and higher taxes on personal income to fund public schools.

In Houston, voters appeared to have rejected a ballot initiative meant to save the stadium that was once their city’s greatest landmark. The Astrodome, touted as the “Eighth Wonder of the World” when it was built in the 1960s, might have been saved (and turned into a convention center) if voters said yes.

They said no. So it will probably face the wrecking ball.