State tacked on a second run an inning later as Andrew Payne deposited an Allard pitch beyond the left-field wall, pushing the Jackets' advantage to 2-0.
Fairmont State (21-24) got on the board in the sixth as Jeff Fansler doubled-home a run to cut State's lead to 2-1. The Falcons had runners on second and third with two out in the inning, but Bowles settled down and escaped the jam.
The Jackets tacked on an insurance run in the eighth as Payne scored Pickering on a single.
West Virginia State advances to play Shepherd at 6:30 p.m. today. The Rams cruised past Davis & Elkins 7-1 in their opener Wednesday. Fairmont State meets D&E at 12:30.
Anthony Pierro went 3 for 5 and Mike Johnson drove in a run for West Liberty.
The Senators touched Hvozdovic for a run in the third inning, but did little else over the next seven innings. Brian Martin kept D&E off the scoreboard in the ninth to close out the win.
Chad Murphy had four hits and drove in three runs for the Rams. Kyle Crist and Matt Barr each had two hits for D&E.