The frontrunners in New Jersey’s gubernatorial race have locked horns on most issues but agree on one thing: No one in the Garden State should ever pump their own gas.

In a rare moment of accord, Congresswoman Mikie Sherill, a Democrat, and a former Republican state assemblyman, Jack Ciattarelli, both said they would retain the state’s unique law that prohibits drivers from filling up their own gas tanks.

“I think a lot of people really love our state laws as they are,” Ms. Sherill said during a debate at Middlesex County on Wednesday. She said she has become quite fond of the state rule since moving from Virginia, “especially when my kids were little, and in the rain.”

Mr. Ciattarelli called the law one of the state’s “special, special differences.”

“Jersey girls don’t like to pump their own gas,” he added, employing a colloquialism that is popular in the state. “We’ll continue at full service.”

The responses provided a moment of levity in an otherwise tense debate between the candidates, who are locked in a tight race ahead of the gubernatorial election on November 4.

Ms. Sherill took her opponent to task for his time operating the medical publishing company Galen, charging that his work there contributed to the opioid epidemic.

“He made his millions by working with some of the worst offenders in saying opioids were safe while tens of thousands of New Jerseyans died,” she said.

That prompted a fiery exchange in which the two shouted “shame on you” at each other.

Shortly afterward, Mr. Ciattarelli cited the release of his rival’s military records, which showed she had failed to blow the whistle on a high-profile cheating scandal while at the U.S. Naval Academy.

“I got to walk at my college graduation, I never broke the law,” he said.

What had been a dead-heat battle between the two candidates began to shift last week, when new polling numbers showed Ms. Sherrill taking the lead.

A Fox News poll showed her ahead of Mr. Ciattarelli among likely voters in the state with a 50 percent to 42 percent advantage. But a Quantus Insights poll released the same day had Ms. Sherrill ahead by just two points.

Among all registered voters, her lead in the Fox News poll was at 48 percent to 41 percent. Both margins exceeded the poll’s sampling error.

The poll also found that 90 percent of Republicans support Mr. Ciattarelli while Democrats support Ms. Sherrill at a rate of 89 percent.