Despaigne's home run off reliever Takeru Imamura at Fukuoka Dome gave Cuba a 6-0 lead. Cuba set up a second-round showdown with Group B runner-up the Netherlands on Friday.
"This is very satisfying," Despaigne said. "This is an important win over Japan that was made possible by making an effort every day. Japan is the two-time champion, and you have to prepare very well to play against Japan."
Japan, which scored three runs in the ninth, will face Group B winner Taiwan in the second round at the Tokyo Dome.
Starter Wilber Perez picked up the win after holding Japan scoreless over three innings. Japan starter Kenji Otonari gave up one run on two hits in three innings to take the loss.
Yasmany Tomas hit a solo homer to left in the bottom of the third to give Cuba a 1-0 lead. Frederich Cepeda doubled in another run in the fourth, and Jose Abreu made it 3-0 on a single to left in the sixth that scored Luis Rivera from third.
Japan has struggled without its top players from Major League Baseball. The three runs in the ninth were more a result of poor pitching by Cuba's relievers, who issued three walks in the final inning.
"We are only looking forward to the next round," Japan manager Koji Yamamoto said. "Although some of our players are not hitting, our pitchers are doing very well."
Cuba, which routed China 12-0 on Monday, displayed the offensive power that makes the 2006 runner-up a title contender this year.
Cuba posted its first win in four WBC games against Japan.
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