Larry Hogan, the popular former governor of Maryland, cruised to an easy victory in the Republican Senate primary on Tuesday, according to The Associated Press, setting up an uncommonly competitive general election contest in the deep-blue state.

Mr. Hogan, a two-term governor from 2015 to 2023 who enjoyed stratospheric approval ratings during much of his time in office, is a vocal critic of former President Donald J. Trump. His race will test whether there is any path forward for anti-Trump Republicans in a party that has remade itself almost wholly in the president’s image.

“The party is still the party of Trump,” he said in an interview on Monday, “but I’m still a voice of reason to try to make sure we get back to a more traditional Republican Party.”

Maryland has not been represented by a Republican in the U.S. Senate since Charles Mathias retired in 1987. The race to replace Senator Ben Cardin, a Democrat who is retiring, was expected to make for a fairly humdrum general election before Mr. Hogan entered the race.

Mr. Hogan said he was driven to run by his frustration over the collapse of a Senate bill that would have paired tough new border security measures with aid for Ukraine and other nations. He announced his campaign in early February and essentially cleared the field of serious competition. It was a recruiting victory for Republicans on top of an already-favorable Senate map across the country this year.

Despite his popularity, Mr. Hogan will still need to persuade the Democrats and independents who have voted for him before to give Republicans another vote in the Senate — and to do so at a time when moderate and liberal voters may be hoping Congress can serve as a check on executive power in case Mr. Trump secures a second term.

In November, Mr. Hogan is likely to face either Representative David Trone, a wealthy businessman who has poured millions of his own money into the Democratic primary, or Angela Alsobrooks, the executive of Prince George’s County.