The 18-year-old struggled to find the plate late, though that was somewhat understandable given the conditions.
Between the time rain started coming down hard and the delay, Greene walked a batter and went to a 3-2 count on first baseman Filiere.
Greene stranded runners at second and third in the first inning.
The game started with Jhonny Bethencourt singling up the middle. Yeiler Peguero then smashed one at shortstop Jose Garcia, who made a nice stop and from his backside threw Bethencourt out at second.
After Filiere crushed a fastball that landed on the warning track in left field for a double, Amaya struck out looking at a 100-mile-per-hour heater to end the frame.
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The Cubs looked ready for the fastball in the second inning, too, as center fielder Chris Singleton made a loud out to left field on a fastball before Greene struck out Rafael Narea on an off-speed pitch.
He went back to the heater to start out Christian Donahue, who hit a laser beam foul down the line. He wore Greene’s next pitch, a fastball that registered 101 on the stadium scoreboard and found Donahue’s thigh.
After he took first base, the inning ended on a check-swing bouncer back to Greene off the bat of Zach Davis.
The Dragons scored three runs in the first off righty Jose Albertos, No. 3 prospect in the Chicago organization according to Baseball America.
The last two came on a 2-run homer by John Sansone that went over the 381 sign in left field.
In two appearances for the Dragons, Greene has struck out 11, walked one and allowed two runs, both earned. He has needed 100 pitches (61 strikes) to get through 5.1 innings.