The Panthers opened the scoring in the game's 25th minute when Carpenter deposited a rebound of Caleb Mulholland's prior shot on goal that bounced away from the goalkeeper.
Later, Greenville added a goal in the 87th minute on a free kick lofted by Bueno.
Goalkeeper Nick Holland picked up his first shutout of the season with a perfect performance in goal. He produced six saves.
Greenville outshot Coe by a 10-9 margin. Each squad had six shots on goal.
Mulholland tallied four shots to lead Greenville.
The Panthers (2-2) had Saturday's game against Robert Morris Springfield postponed, and it has yet to be rescheduled. They will return to action on Wednesday at 7 p.m. when Millikin visits Greenville.