Zak Borenstein ran home for a fourth in the eighth innings from a Blaker Gailen hit, while tight pitching prevented the Cubans from scoring.
Borenstein said: "We didn't light up the scoreboard today but we were able to get the timely hits when we needed them.
"Things are just clicking for us right now."
“We’ve pitched extremely well and have had timely hitting and good defence,” Israel manager Jerry Weinstein said.
“I am happy we were able to defeat one of the premier teams in international baseball.”
Israel will take on the Netherlands, who they beat in the first round in Seoul, on Monday in an attempt to maintain their winning streak, with the top two teams progressing to next week's semi-finals in Los Angeles.
Additional reporting by Simon Griver
