Lone Star Conference Co-Player of the Week Chuck Duarte ended the game with one out in the seventh after slicing a bases-clearing double down the left-field line. Duarte finished the game 2 for 3 with four RBI.
The victory lifted ACU's record to 23-19, while the Falcons fell to 11-28.
The Wildcats trailed early in the first when left fielder Ryne Head scored on a two-out RBI single, but starter Austin Palmer settled down afterward and gave up just two more hits over the next 3.0 innings while striking out five.
Josh Stone (5-4) relieved Palmer to start the fifth and delivered 2.0 scoreless frames with two Ks, and then Emmett Niland came in to pitch the seventh, leaving a runner stranded at third base.
The Wildcats took the lead for good in the third as they scored six times off Falcon relievers Cory Blackmon (0-1) and Casey Rana, each of who exhibited some control issues.
After Luke Mejia grounded out to begin the inning, the next three Wildcats all singled and then Duarte gave the home team a 2-1 lead with a fly ball to center. Blackmon couldn't get the final out as he walked the next two hitters in loading the bases, and Rana wasn't much help either as he immediately surrendered a two-run single by Reed Watson.
Rana walked the next three batters, which pushed the ACU lead to 6-1, before finally getting Kyle Conwell on a fly ball to left.
Tyler Eager singled to lead off the fourth and made it a 7-1 game after scoring on one of three Jeff Fisher-Gasper wild pitches, and in the sixth, Duncan Blades singled home Rodge Macy from third.
Mejia started the seventh with a single to center off reliever Josh Wise, who then issued back-to-back walks with one out before giving up the game-ending hit to Duarte.
The Wildcats return to action Friday night when they play host to Tarleton State at 7 p.m.