Mr. Cox will face the winner of the crowded Democratic primary, which featured state comptroller Peter Franchot, former nonprofit CEO Wes Moore and former U.S. Labor Secretary Tom Perez.
Mr. Moore had climbed out to an early lead and the race was called by multiple news networks about three hours after the polls closed at 8 p.m.
With an estimated 60.4% of the Republican primary vote counted, Mr. Cox held a 56.3% to 40.2% lead over former state Labor Secretary Kelly Schulz in the four-person race.
The Cox victory will be viewed as a black eye for Gov. Larry Hogan and is going to be billed as good news for Democrats in what is otherwise shaping up to be a tough midterm election.
Mr. Hogan, who is term-limited and cannot run, endorsed Ms. Schulz this year, telling voters if they approve of the job he did as governor, then she is their choice. Ms. Schulz served as secretary of labor and commerce in the Hogan administration.
Things were still up in the air on the Democratic side.
With an estimated 39% of the vote counted in the Democratic race, Mr. Moore had received 37.3% of the vote, followed by Mr. Perez at 26.3% and Mr. Franchot at 20.2%.
The official winner in that race might not be known for days.
The delay is due to the fact that mail-in voting in Maryland has exploded in popularity and local election officials are barred from reviewing and tallying up those voters until two days after the election.
Nearly 500,000 mail-in ballots were requested and sent to voters, including over 370,000 to Democrats and over 86,000 to Republicans.
Mr. Cox’s victory will go a long way in testing how much of an appetite there is for a Trump-endorsed candidate in a deep blue state that embraced Mr. Hogan’s moderate message in back-to-back elections.
Mr. Cox, however, ran hisGOP primary campaign by contrasting himself with Mr. Hogan, slamming his response to the coronavirus.
GOP voters rallied behind that message, tossing aside concerns about his electability.
Democrats are betting he will scare off middle-of-the-road voters.
Democrats are betting his Trump-inspired brand of politics will turn off most voters in the liberal-leaning state that, among other things, has handed double-digit defeats to every Republican presidential nominee since George H.W. Bush in 1992.
• Seth McLaughlin can be reached at email@example.com.
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