The Dominicans thus joined Japan and the Netherlands in the semifinals of the world tournament. The fourth semifinal spot will be determined on Friday when the United States takes on Puerto Rico in an elimination game.
The Americans scored their only run in the first inning on a bases-loaded walk drawn by Eric Hosmer, but they wasted a chance for a big inning when they left the bases jammed.
A home run in the second by Hanley Rodriguez lifted the Dominican Republic into a 1-1 tie and it stayed that way until the ninth.
Aybar's single to right drove in Cruz with the go-ahead run and Aybar later stole second, from where he scored on the base hit from Reyes.
Both ninth-inning runs were charged to Craig Kimbrel. Pedro Strop worked a perfect eighth inning for the Dominicans to get the win and Fernando Rodney retired the side in order in the ninth for the save.
The United States defeated Puerto Rico 7-1 in the opening game of the double-elimination phase of the tournament, but will need another win to keep alive its hopes for a world championship.