In the first game of the doubleheader, Cedric Sabin had two goals five minutes apart late in the first half and paced Martinique - which finished with 10 men -- past Puerto Rico 2-1.
Fana scored in injury time of both halves, in the 46th and 93rd minutes, to give the Dominican Republic a third straight victory in the Caribbean Cup and extend its unbeaten streak overall to seven matches. It has not lost since a 2-1 defeat to El Salvador in the second round of World Cup qualifying in July 2011.
It also was the second straight match that Fana had scored twice, having lifted the Dominican Republic past Dominica 2-1 a month ago to send it to the second round of the Caribbean Cup.
The match was the first competitive game for Guadeloupe since it lost all three matches at last year's CONCACAF Gold Cup and extended its winless streak to five.
Earlier, Sabin converted a penalty in the 38th and added a second goal in the 43rd to stake Martinique to a 2-0 lead. Hector Ramos pulled Puerto Rico within a goal in the 55th. Martinique was reduced to 10 men with three minutes remaining when Steeve Penel was ejected for stomping on an opponent.
Alexis Rivera also was red carded, but after the match, for approaching St. Vincent referee Caswell Cambridge and berating him.
The victory kept Martinique, which began the Caribbean Cup qualifying with a 16-0 victory over British Virgin Islands unbeaten in the competition in its four games and five overall.