Tomas hit a solo home run in the third inning and Despaigne sealed the game with a three-run shot in the eighth as Cuba completed Pool A play 3-0. However, Japan, 2-1 in the group, still joins Cuba in advancing to the WBC second round.
Cuban pitching allowed just two runs -- both unearned -- in round-robin play until the ninth inning Wednesday, when Japan used three walks, an infield hit, a sacrifice fly and a ground-ball single for its runs.
Wilbur Perez (1-0) started for Cuba and allowed three hits and one walk while striking out three in three innings. Six more Cuban pitchers, including Vladimir Garcia who got the final two outs, gave up four hits and five walks over six innings.
Tomas hit the second pitch from Japan's Kenji Otonari (0-1) in the third inning deep into the seats beyond left-center for the game's first run. Frederich Cepeda doubled in a run in the fourth and Cuba went up 3-0 with Jose Abreu's sixth-inning RBI single.
Takeru Imamura came in to pitch for Japan in the eighth but walked Cepeda with one out. Abreu followed with a single before Despaigne's blast to center.
Japan, which won the first two WBC titles, meets Taiwan in the first second-round game Friday while Cuba will play the Netherlands. The second-round Pool 1 is a double-elimination tournament in Tokyo.