The Texans go on to face the Rams in the championship round, where they'll have to win twice in order to earn a NCAA postseason berth. The Wildcats' season, meanwhile, ends at 26-28.
ACU had several chances to stave off elimination, but the Wildcats couldn't come up with a second clutch hit past Travis Schuetze's go-ahead double in the fourth.
That lead, however, lasted just a half inning as the Texans were aided by a Duncan Blades' error at third.
Ty Crump led off with a single and was bunted over to second. Blades then handled a sharp ground ball hit by Small, but after looking Crump back to the bag, he airmailed the throw over the head of first baseman Tyler Eager.
Crump was held at third on Blades' miscue, but eventually tied the score at 2-2 on Andrew Wolfe's fly ball to center. Kevin Finklea attempted to gun Crump out at the plate, but his throw was cut off at the mound by Eager, who then flipped the ball back to second where Schuetze put the tag on Small diving back.
An inning later, the Wildcats placed a runner at second base with two outs and Ryan Luckie at the plate. Luckie lofted a sofT line drive to shallow right that went over the head of first baseman Garrett Hardey, but Small made a terrific sliding catch on the grass right as the ball was ready to hit the ground.
Then when it was Small's turn to hit in the seventh, he drove the ball far enough to left field to plate the game-winning run on a sacrifice fly. Landon Thompson, who recorded the first of three hits in that fateful inning, scored on the play.
ACU starter Brady Rodriguez was saddled with the loss despite striking out three and stranding five base runners over 7.0 solid innings of work.
Clint Cooper pitched a scoreless eighth for the Wildcats.
The Texans took the game's first lead in the second after Thompson singled home Jonathan Schmitz with a one-out shot to left. Rodriguez, however, responded to the run by getting Chris Patton to ground out, and then punched out Ty Crump to end the inning.
Schuetze gave ACU its first and only lead in the fourth. Reed Watson began the rally with a two-out single to center, which was followed by a walk to Luckie. Schuetze then drilled a two-run double to left just over the reach of Patton.
Austin Coble, in his first start of the year for Tarleton, went 6.0 strong with four strikeouts before giving way to Britt Robertshaw to begin the seventh.
Coble escaped a bases-loaded jam in the second by getting Luckie to ground into a 6-4-3 double play, and then left runners stranded at the corners in the third.
Robertshaw, in earning the victory, allowed no hits in his 3.0 innings of work.