Devron Garcia secured a brace in the first half for the Central Americans, who added insurance goals by Brayan Velasquez and Rembrandt Flores in the second half at Estadio Rommel Fernandez.
The Cubans (0-0-2, 0 pts), who dropped a 5-1 decision to Mexico on Sunday, were eliminated from the competition. Honduras (1-0-0, 3 pts.) will meet Mexico (1-0-0, 3 pts.) for the group title on Thursday.
The Hondurans enjoyed the early run of play, taking two shots in the opening four minutes -- a 35-yard blast from Luis Santos that sailed wide left in the third minute and a header from inside the penalty area that was saved by goalkeeper Silvio Bell a minute later.
But the Cubans settled down and to assert themselves. It paid off in the 17th minute. A ball was lofted into the area and Reinier Arencibia headed it out to Yorjandy Somonte, who snapped an 18-yard bullet to the lower right corner for a 1-0 advantage.
Ten minutes later, Honduras equalized. Bell produced a nice kick save of a close-range shot, but the ball went straight to Garcia, who converted the rebound past a sprawled Bell to tie things up at 1-1.
Bell was tested several more times in the opening half. In the 31st minute. Velasquez fired an eight-yard shot that the Cuban keeper managed to knock out of harm's way.
Bell wasn't as fortunate three minutes later as he left another rebound that changed the course of the game. Kevin Alvarez sent the ball into the box to Alberth Elis, who turned and launched a 10-yard shot that Bell blocked with both hands. Again, the rebound came to Garcia, who put it home for a 2-1 lead.
Los Catrachos came close to extending their lead in the 37th minute as Kevin Alvarez looped in a long free kick that hit the crossbar.
Cuba came close to tying things up in the 45th minute as Arencibia put a close-range shot off his right thigh to goalkeeper Cristian Hernandez.
With the second half barely three minutes old, Velasquez gave the Central American side some breathing room. Elis, who had the ball in traffic in the middle of the box, sent a short pass to his right to Velasquez, who powered a shot to the lower right corner for a 3-1 lead.
Velasquez almost collected his second goal of the half in the 71st minute as he slammed an 18-yard blast off the crossbar. He injured his left leg on the play and was replaced by Darwin Arita in the 75th minute.
Flores completed the scoring in the 87th minute, when he beat Bell from a difficult angle on the left side.