While they may be fretting about Donald Trump’s presidential nomination, Republican congressional leaders are breathing a sigh of relief Tuesday for their own colleagues.

Even as Trump appeared on his way to winning three or four of the five states holding presidential primaries Tuesday, Republican senators up for re-election in several of those states easily bested primary challengers who had hoped to ride Trump’s coattails to victory. And Senate Democrats’ chosen candidates to challenge Republicans this fall — several of them current or former lawmakers themselves — didn’t have any problem in their primaries either.

Republican incumbents’ ability to hang on while sharing a ballot with Trump bodes well for Republicans trying to keep the Senate and better their cushions in the House of Representatives and in governors’ mansions. So far, congressional primaries from Alabama to Illinois are suggesting that the same voters who want a political newbie in the White House just might be OK with sending a veteran back to Congress to work with him.

Here’s a rundown of the night’s notable primary results.

– North Carolina

The man who has been in the Senate a decade had no problem besting a challenger who campaigned with a bus emblazoned “Defeat the Washington Establishment.” Sen. Richard Burr, R-N.C., beat former congressional candidate Greg Brannon by a nearly 3-to-1 margin on Tuesday.

Burr will face former state representative Deborah Ross, who won her Democratic primary Tuesday, in November. She isn’t Democrats’ dream candidate, but it’s a race that has the potential to be competitive. Outside groups on both sides are expected to spend big to tip the scales.

The battle lines are also formed in North Carolina’s governor’s race, which is ranked fourth in our top five competitive governor’s races this fall. Republican Pat McCrory beat two-little known candidates handily, including a former state representative who ran as an outsider.

Roy Cooper, North Carolina’s longtime attorney general who won his Democratic primary on Tuesday, will try to stop McCrory from getting a second term. Financially, Cooper is set up well for a fight: He has out-raised McCrory for 14 months in a row; most recently touting he has $1.4 million in the bank more than the governor. This is a close race that will likely hinge on presidential politics.

– Illinois

In Illinois, one of the year’s marquee Senate races also went according to expectations.

Two-term Rep. Tammy Duckworth (D) will challenge one of Republicans’ most vulnerable senators up for reelection this fall, Sen. Mark Kirk, R-Ill. Duckworth easily beat her challengers, Chicago Urban League CEO Andrea Zopp and state Sen. Napoleon Harris, a former NFL player. (Though Zopp outperformed expectations by registering almost a third of the vote, more than twice what some public polls had predicted.)

Kirk easily won his primary against a nominal challenger, but a Chicago Tribune poll taken ahead of the primary shows he may have some work to do to rally his base in November. Barely half of Republican voters have a favorable view of Kirk, while 7 in 10 Democratic voters like his opponent, Duckworth.

– Ohio

A similar situation played out Tuesday in Ohio, where a Republican incumbent senator and his Democratic challenger — both big names in the state — won their primaries and will go onto challenge each other for one of the nation’s most hotly contested Senate seats in November. Sen. Rob Portman (R) easily bested a little-known Christian conservative candidate who tried to make Portman’s support for same-sex marriage a campaign issue.

Former Democratic Ohio governor Ted Strickland had no problem with a vigorous challenge from the much-younger P.G. Sittenfeld, a 31-year-old Cincinnati councilman who tried to make Strickland’s support for certain gun rights a campaign issue. Sittenfeld had picked up newspaper endorsements from two of Ohio’s major newspapers, but President Obama and Vice President Joe Biden endorsed the former governor in the days before the primary.

– House races

Most of the underdog Senate primary candidates were trying to toss out an incumbent without much outside help. But in Illinois’s 15th congressional district, tea party candidate and state Sen. Kyle McCarter actually had help in the form of ads and an endorsement from conservative grassroots group Club for Growth, which endorsed him over GOP Rep. John Shimkus, a 20-year veteran in Congress.

Shimkus held a very early lead on Tuesday night, and if he were to win, he’d win a likely 11th term in Congress in November.

But the Club for Growth was doing much better in the less-defined, crowded House race in Ohio for former House speaker John Boehner’s old seat. No fewer than 17 candidates were trying to take it for the first time it’s been open in nearly 25 years. The winner of a June special election will serve out the rest of 2016 in Boehner’s seat.

With 81 percent of precincts reporting, Club for Growth-backed tea party candidate Warren Davidson was leading with 33 percent of the vote, at least eight points ahead of two of his biggest challengers: the more moderate candidates state Sen. Bill Beagle and state Rep. Tim Derickson. A tea party candidate winning Boehner’s seat would be a symbolic victory of the faction of that party, given its antagonism toward Boehner. This is a strong Republican district, so the winner of the primary should hold the seat going forward.

(c) 2016, The Washington Post · Amber Phillips