Jones reached on an error with one out in the ninth and the Netherlands loaded the bases with singles by Curt Smith and Xander Bogaerts.
Diosdany Castillo was brought in to pitch to Kalian Sams, who hit a 1-2 pitch to deep center, allowing Jones to easily score the winning run.
The Netherlands joins Japan in qualifying for the WBC semifinals next week in San Francisco. Japan, the two-time defending WNBC champion, and the Dutch will play Tuesday to decide which team is the top seed from Pool 1. Japan beat the Netherlands 16-4 earlier in the tournament.
The other semifinalists will come from a double-elimination round involving the Dominican Republic, Italy, Puerto Rico and the United States.
Loek Van Mil (1-0) pitched around a self-made jam in the ninth and got the win for the Netherlands. Yander Guevara (0-1) allowed Jones and Smith to reach, touching off the winning rally.
Cuba twice erased two-run deficits with Jose Abreu hitting a home run in the fourth and Yulieski Gourriel a two-run double for a 4-4 tie in the fifth.
The Cubans went up in the eighth when Yasmany Tomas singled in a run and Eriel Sanchez hit a sacrifice fly. But the Netherlands answered with a two-run Andrelton Simmons home run that tied the score.
Jones, a five-time U.S. major league all-star who now plays in Japan, was born in Curacao, a constituent country of the Netherlands.
Swim Week Miami Beach 2014 [PHOTOS]