Rodriguez tossed six scoreless innings, allowing two hits and walking two, in the Dominicans' 2-0 victory over Puerto Rico at Marlins Park in Miami.
The 34-year-old left-hander also struck out four. He threw 74 pitches, 49 for strikes.
The victory gives the Dominican Republic the top seed in Pool 2. The Dominicans now face the Kingdom of the Netherlands on Monday at AT&T Park in San Francisco. Puerto Rico will face Japan on Sunday in San Francisco.
Rodriguez allowed four of the six leadoff batters he faced to reach, but he faced little trouble outside of the third inning.
The biggest threat against the lefty came in the top of the third, when Puerto Rico's Carlos Rivera collected the game's first hit, a single. Irving Falu entered to pinch-run for Rivera and promptly stole second, then advanced to third when catcher Carlos Santana's throw went into the outfield.
With one out, Jesus Feliciano hit a grounder to shortstop Erick Aybar, who threw out Falu at home, as the Dominicans escaped the jam.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.