Republican voters in Iowa dealt a shock defeat to President Trump on Tuesday, narrowly rejecting his chosen candidate for governor in favor of another conservative contender who ran as a political outsider.

The primary loss for Representative Randy Feenstra, whom the president endorsed on Friday afternoon, came at a time of mixed signals of Mr. Trump’s power over the Republican Party. He has won a series of dominant primary victories over Republican opponents, but has faced rising pushback from his party in Congress.

Here are four takeaways from a busy primary night in Iowa and several other states. (You can follow California’s high-stakes primaries here.)

Trump had a rare high-profile primary loss.

In modern Republican primary politics, Mr. Trump’s endorsement is the gold standard. In the last month, it has ousted sitting senators, a congressman and state legislators whom the president deemed insufficiently loyal.

So when Mr. Feenstra won Mr. Trump’s endorsement for governor last week, it felt like the push he needed to get past four candidates in the primary.

Yet Mr. Feenstra was toppled on Tuesday by Zach Lahn, a conservative political operative and farmer who ran an insurgent campaign. Mr. Feenstra was seen as having run a lackluster campaign, and also faced the wrath of former Representative Steve King, who lost to Mr. Feenstra in a 2020 primary and backed Mr. Lahn.

Mr. Feenstra’s defeat makes him the highest-profile candidate endorsed by Mr. Trump to lose a Republican primary race in years — perhaps since Luther Strange, an appointed senator in Alabama, fell to Roy Moore in a 2017 special election primary. Mr. Moore went on to lose the general election to Doug Jones, a Democrat.

Mr. Feenstra was widely seen as having run a lackluster campaign that failed to win over the state’s conservative base. Mr. Trump’s endorsement was most likely just too late — there was no time to produce television ads highlighting it in the final days before the primary.

The result sets up a general election that Democrats believe is their best chance to flip a governorship. The Democrat in the race is Rob Sand, the state auditor, who is mounting a well-funded campaign to succeed Gov. Kim Reynolds, who did not seek re-election. No Democrat has won election as Iowa governor since 2006.

A Democrat seen as Schumer’s pick won in Iowa.

Josh Turek, a Paralympic gold medalist who was backed by $10 million from a group allied with Senator Chuck Schumer of New York, the minority leader, coasted to victory in Iowa’s Democratic primary for Senate. He defeated Zach Wahls, a progressive state senator who ran a campaign aimed at upending the party establishment.

Mr. Turek gives Democrats a Senate nominee with experience winning state legislative races on Republican turf. He will face Representative Ashley Hinson, a Republican, in the general election to succeed Senator Joni Ernst, a retiring two-term Republican.

Democrats need to hold their own Senate seats and flip at least four G.O.P.-held seats to take a majority in the chamber.

Mr. Turek’s primary triumph demonstrated that despite Democratic voters’ anger toward their leaders in Washington, it remains difficult for an insurgent candidate to overcome a big financial disadvantage.

Mr. Wahls, a former State Senate minority leader, ran as a political outsider who aimed to upend the Washington establishment, pledging to vote against Mr. Schumer as Senate Democratic leader.

In the end, the $10 million from VoteVets, a Schumer-aligned Democratic veterans organization, was too much for Mr. Wahls to overcome.

A progressive prevailed in a crowded New Jersey primary.

Dr. Adam Hamawy, who was endorsed by Senator Bernie Sanders of Vermont and Representative Alexandria Ocasio-Cortez of New York, won a crowded Democratic primary for a deep-blue House district in central New Jersey.

A retired Army surgeon, Dr. Hamawy is best known for helping to save the life of Tammy Duckworth, now a senator from Illinois. He is running to succeed Representative Bonnie Watson Coleman, who did not seek re-election.

Dr. Hamawy is the second progressive to win a contested New Jersey primary this year. In a February primary, Analilia Mejia, a political organizer who was also endorsed by Mr. Sanders and Ms. Ocasio-Cortez, surprised political observers in the state by winning a special-election primary. Ms. Mejia coasted to a primary victory on Tuesday.

A Biden alumna cruised in New Mexico.

Deb Haaland, who served as interior secretary during the Biden administration, won an easy victory in the Democratic primary for governor of New Mexico without an endorsement from the former president.

Ms. Haaland dispatched Sam Bregman, a local prosecutor who tried to run an anti-establishment campaign. Mr. Bregman is the father of the Chicago Cubs third baseman Alex Bregman.