One candidate for governor of New Jersey was arrested. Another won a coveted endorsement from President Trump. And the rules that for decades governed primaries in the state were deemed unconstitutional, shattering the traditional playbook for all the candidates hoping to be elected the next governor.

At 6 a.m. on Tuesday, voters began casting their final primary ballots, closing a yearslong chapter in an extraordinary election cycle.

The winners of the Democratic and Republican primaries will compete in November’s general election after a race heavily influenced by external forces.

After lawsuits and a ruling by a federal judge, the names of six Democrats and five Republicans vying for their party’s nomination were printed on ballots redesigned to diminish the power of county political bosses. The candidates competed for attention from a shrinking number of news outlets. And the messages they delivered were frequently overshadowed by the upheaval in Washington that has defined the first five months of Mr. Trump’s second term as president.

Lauren Welch, 43, moved to New Jersey from Washington, D.C., about two years ago, and said she was excited to cast a vote Tuesday in an election that was not a foregone conclusion.

“I know it’s going to be a close race in November,” said Ms. Welch, a Democrat, “so I voted for the person I felt was most likely to win.”