Former Republican governor Charlie Crist (L), now running for the Democrats, addressing supporters during a rally in St. Petersburg, Fla., Nov. 4, 2013, and Florida Republican Gov. Rick Scott speaking at a ceremony in Doral, Fla., on Aug. 28, 2013. (REUTERS/Steve Nesius/Joe Skipper)

This post has been updated

Florida Gov. Rick Scott (R) and former governor Charlie Crist (D) easily won their primary elections Tuesday, advancing to a general election showdown that is expected to be one of the nastiest and most expensive campaigns in recent history.

Faced with only nominal competitors, both were declared victorious not long after the polls closed Tuesday evening. Crist had no trouble getting past Nan Rich, a former state senator. Scott breezed by Puerto Rican Chamber of Commerce of Florida founder Elizabeth Cuevas-Neunder and pharmacist Yinka Adeshina.

(Live results in Arizona, Florida, Oklahoma and Vermont)

With exactly 10 weeks to go until the election, Scott and Crist officially kicked off a bitter confrontation that has effectively been underway for months. Republicans have been trying to cast Crist, a former Republican and independent, as a shape-shifting opportunist. Democrats have portrayed Scott as an extremist and ineffective leader. Scott’s campaign spending could top $100 million.

Former Florida governor Charlie Crist won the Democratic gubernatorial primary on Tuesday, setting him up for a November run against incumbent Republican Gov. Rick Scott. (YouTube/Charlie Crist)

Florida was one of four states where voters went to the polls Tuesday. In Arizona, they pared down the field in the first open governor’s race in 12 years. In Oklahoma and Vermont, lower-profile contests were being settled.

Arizona Treasurer Doug Ducey won the Republican nomination to succeed outgoing Gov. Jan Brewer (R). He defeated former Mesa mayor Scott Smith. former GoDaddy executive Christine Jones and three other candidates. He will be favored to defeat Democrat Fred DuVal, who was unopposed in the primary.

Ducey, a former Cold Stone Creamery chief executive, was backed by numerous national tea party leaders including Sarah Palin and Sens. Ted Cruz (R-Tex.) and Mike Lee (R-Utah). Smith, a more moderate Republican, had Brewer’s backing. The governor campaigned hard for him in the closing stage of this race.

A handful of primaries in U.S. House districts in Arizona were also under close watch by national political strategists.

In the 1st district, where Democratic Rep. Ann Kirkpatrick is vulnerable, state House Speaker Andy Tobin, the choice of the GOP establishment, was running slightly ahead of rancher Gary Kiehne and state Rep. Adam Kwasman, with about a quarter of the vote tallied. Most strategists considered Kwasman and Kiehne less electable choices.

In the heavily Democratic 7th district, where Rep. Ed Pastor (D) is retiring, former state representative Ruben Gallego defeated former Maricopa County supervisor Mary Rose Wilcox. Gallego will be a near sure bet in November; Republicans did not even field a candidate.

Meanwhile, in the 2nd district, where Rep. Ron Barber (D) is one of the most vulnerable incumbents in the country, retired Air Force colonel Martha McSally won the Republican nomination, setting up a rematch. Barber barely defeated McSally in 2012.

Oklahoma held runoff elections to settle primaries in which no candidate received a majority of the vote. The marquee contest was the Republican race in the 5th district, safely GOP territory where Rep. James Lankford (R) is leaving to run for the U.S. Senate.  Former state senator Steve Russell defeated Oklahoma Corporation Commissioner Patrice Douglas. He will be an overwhelming favorite in November.

In Florida’s 26th district, where Republicans believe they can unseat Rep. Joe Garcia (D), Miami-Dade School Board member Carlos Curbelo won the GOP nomination. He outpaced four opponents on the ballot – including embattled former congressman David Rivera, who suspended his campaign in July.