It was the biggest primary night since Super Tuesday, and there were few surprises in the results.

Bernie Moreno won the Republican Senate primary in Ohio, wielding the powerful endorsement of former President Donald J. Trump to become the Republican nominee in perhaps the most consequential race in the battle for the Senate this November.

Incumbent representatives also fended off primary challenges in Illinois, and the results of a special primary in California will, eventually, decide who completes the term of former House Speaker Kevin McCarthy, who was ousted from his post last year and left Congress not long after.

Here are four takeaways.

Bernie Moreno, a wealthy former car dealer and political newcomer, emerged victorious from a three-way brawl in the Ohio Republican primary to determine who would take on Sherrod Brown, the Democratic incumbent, in an increasingly Republican state.

The hotly contested primary proved once again just how powerful an endorsement from Mr. Trump is, especially in a state like Ohio. The former president backed Mr. Moreno early, while the Republican establishment tried mightily to lift its chosen candidate, Matt Dolan, a wealthy state senator.

But the star power of Ohio’s Republican governor, Mike DeWine, and its former moderate senator, Rob Portman, was decisively outshone by Mr. Trump. Mr. Moreno cruised to victory, earning a narrow majority of the vote in a three-way race.