The host Wildcats committed four errors that led to two unearned runs for the Hillbillies.
Nick Carter doubled for Man, which improved to 22-9 on the season with the win.
Timmy Rein went 3-for-4 with a double for Logan, which dropped to 19-11.
Ryan Butcher also had two hits, including a double, for Logan.
Logan still took the season series with the Billies two games to one. The Wildcats beat Man this season by scores of 11-2 and 3-1.