Urena, in for the injured Bryan Ruiz in the Costa Rica attack, opening the scoring in the Group A encounter in the seventh minute with a smart, close range finish at the near post after good work down the left from Christian Bolanos.
Cuba went close to an equaliser just moments later when Alain Cervantes found Albert Gomez with a delightful pass but the striker lifted his shot over the bar.
Cuba's discipline in defence fell apart though a minute after the restart when an unmarked Urena raced on to a long ball over the top and rounded Molina to make it 3-0.
"Obviously I am pleased with the result but there are still some things to work on," said La Volpe.
"We need to be more precise in certain areas," said the former Mexico coach, who had been booed by Mexico fans in the stadium ahead of their team's game against El Salvador.
Every time La Volpe's face appeared on the giant screen at the stadium there were whistles and jeers but the coach, who was in charge of Mexico from 2002 to 2006, laughed off the abuse.
"If they are booing me, I'd hate to think what they would do to some of their other coaches," he said.
"We will have to work hard to get ourselves right emotionally for that game and these five goals certainly don't help," he said.
