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.
That was the last chance of any real note from the Cubans, who, playing on the unfamiliar artificial surface, were outclassed by a Costa Rica side coached by the experienced Argentine Ricardo La Volpe.
The impressive Alvaro Saborio hit the post with a well-struck shot from the edge of the area before he got on the score-sheet four minutes before the break - latching on to a long ball from Bolanos and slotting past Odelin Molina in the Cuban goal.
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.
Just a minute later and it was virtually a carbon copy goal as the busy Heiner Mora this time found himself alone behind the Cuban back line and also rounded the keeper before slotting home.
It was one-way traffic from then on and Costa Rica did their goal difference no harm when Mora broke down the right and his cross to the back post was met by substitute Joe Campbell, who blasted the ball into the far corner.
"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.
Cuba head coach Raul Gonzalez now has the unenviable task of preparing his team to face group favourites Mexico.
"We will have to work hard to get ourselves right emotionally for that game and these five goals certainly don't help," he said.
