Sams' deep fly ball to centerfield off Cuba reliever Diosdany Castillo at Tokyo Dome allowed Andruw Jones to score from third and touched off a wild celebration by the Netherlands, which becomes the first team from Europe to reach the semifinals.
"This game will go down as the biggest game in Dutch history," Netherlands manager Hensley Muelens said. "To come back like that after being down in the eighth is amazing."
Sams played for Everett in 2007, 2009 and 2010.
Andrelton Simmons hit a two-run homer off Cuba reliever Norberto Gonzalez in the bottom of the eighth to tie the game at 6-6 just after Cuba had taken a 6-4 lead in the top of the inning.
"I felt like I had to step up," Simmons said. "He gave me a pitch to hit and I was really happy I could tie the game for us."
The Netherlands will join defending champion Japan in the March 17-19 championship round in San Francisco.
Yasmany Tomas hit a single to right field in the top of the eighth that broke a 4-4 tie and Cuba added an insurance run with a sacrifice fly to left field by catcher Eriel Sanchez.
The Netherlands took a 2-0 lead in the third. Jones hit a bases-loaded sacrifice fly to left and Curt Smith hit an RBI single to left, scoring the runner from second.
But Cuba tied the game in the top of the fourth when Jose Fernandez singled on a line drive to right to score Yulieski Gurriel and Jose Abreu hit a solo homer over the centerfield wall, chasing Dutch starter Orlando Yntema.
The Netherlands regained the lead with two runs in the fourth. Simmons hit a sacrifice fly to left scoring Sams and the Dutch added another when Randolph Oduber stole third base and scored on a throwing error by catcher Frank Morejon.
Gurriel doubled in two runs in the fifth to tie the game 4-4.
The Netherlands beat Cuba 6-2 in the first game of the second round.
"I told the guys before the game the better team will win and tonight the better team won," Muelens said. "The guys were resilient and stayed together and that's why we won."
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