WASHINGTON — North Carolina House Speaker Thom Tillis captured the Republican nomination to oppose imperiled Democratic Sen. Kay Hagan Tuesday night, overcoming anti-establishment rivals by a comfortable margin in the first of a springtime spate of primaries testing the strength of a tea party movement that first rocked the GOP four years ago.

In Ohio, Cuyahoga County Executive Ed FitzGerald won the Democratic nomination to challenge Gov. John Kasich in the fall. U.S. House Speaker John Boehner, a Republican, rolled to renomination for another term in Congress, his 13th.

On a night that was kind to Republican incumbents in three states, GOP Rep. Susan Brooks of Indiana easily fended off a challenge from the right, rolling up 75 percent of the votes in a three-way race. First-term Rep. David Joyce of Ohio had a slightly tougher time but was running well ahead of his tea party rival.

Anti-war Republican Rep. Walter Jones defeated his challenger in North Carolina.

In North Carolina, Tillis was winning about 45 percent of the vote with ballots counted in 72 percent of the state’s precincts, easily surpassing the 40 percent needed to avoid a July runoff. Greg Brannon was trailing despite support from tea party favorite Sen. Rand Paul of Kentucky.

Also in North Carolina, former “American Idol” runner-up Clay Aiken had a narrow lead as he sought the Democratic nomination to oppose Republican Rep. Renee Ellmers in the fall. A Democratic runoff was possible.

Democratic State Rep. Alma Adams was comfortably ahead for a pair of nominations at the same time: in a special election to fill the unexpired term of former Rep. Mel Watt, and also for the November ballot in the heavily Democratic district.

Tuesday marked the beginning of the political primary season in earnest, and over the next several months Republicans will hold numerous contests featuring incumbents or other establishment figures against tea party challengers. Some of the races are in states where the identity of the party’s candidate might mean the difference between victory and defeat this fall, such as Alaska, Georgia, Iowa and Kentucky, as well as North Carolina. In other areas, it will matter less, including Kansas, Mississippi, Nebraska, Oklahoma and South Carolina.