It started with a coin toss and ended with a song request. But in the hour between, the first and only debate between Gov. Andrew M. Cuomo and his Republican opponent, Marcus J. Molinaro, devolved into a shouting match in which discussions about New York’s challenges were largely eclipsed by name-calling and aspersions about the other’s record.

Mr. Molinaro tried to seize his hour of prime-time television (the debate, held Tuesday afternoon at the CBS studios in Manhattan, was aired on tape delay at 7 p.m.) to highlight the corruption and tax increases that he said have been endemic to the current administration. Mr. Cuomo batted away those attacks, focusing instead on casting Mr. Molinaro, a former state assemblyman and current Dutchess County executive, as a devotee of President Trump.

“Do you support Donald Trump?” Mr. Cuomo asked Mr. Molinaro at least four times, ignoring the moderators’ attempts to rein him in — a tactic repeatedly adopted by both men.

“Let’s get out of this conversation,” Mr. Molinaro replied.

“Do you support Donald Trump?” Mr. Cuomo pressed again. “You can’t answer it.”