Johnson grabbed 11 rebounds and E'Twaun Moore added 17 points, collected six caroms and made four steals for the Boilermakers (4-0).
Ryne Smith chipped in with 11 points and D.J. Byrd contributed 10 for the victors, who outscored Austin Peay 9-2 to start the second half, forging a 15-point lead.
The Governors (2-3) were led by Tyshawn Edmondson with 16 points while John Fraley put in 11 points and grabbed 13 rebounds in the loss.
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