The Netherlands, the first European team to reach the final four, advanced along with two-time defending champion Japan. At the semifinals in San Francisco on March 17-18, they will be joined by two teams from among the United States, Dominican Republic, Puerto Rico and Italy.
"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."
The Dutch had beaten Cuba 6-2 in the opening 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."
"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."
Loek Van Mil, the fourth Dutch pitcher, got the win with a two-hit ninth.
Jones' bases-loaded sacrifice fly and Smith's RBI single put the Dutch ahead in the third, but Jose Fernandez's RBI single and Jose Abreu's homer off Netherlands starter Orlando Yntema tied the score in the fourth.
The Dutch took a 4-2 lead in the bottom half when Simmons hit a sacrifice fly, and Randolph Oduber stole third and scored on catcher Frank Morejon's throwing error.
Gourriel retied it with a two-run double in the fifth.