Lamar could not slow SHSU's rushing attack as the Bearkats totaled 268 yards. Jalen Overstreet ran for 132 yards on nine carries.
SHSU (2-3, 1-0) was ahead 19-3 at the half. Lamar's Caleb Berry hit Mark Roberts on a 32-yard scoring strike with 9:05 remaining in the third quarter to close the gap.
The Bearkats responded quickly when Johnson passed to Gerald Thomas from the 22 for a score and a 26-10 advantage.
Overstreet dashed 50 yards for a score in the fourth to seal the victory.
Berry threw for 244 yards and one touchdown for Lamar (3-2, 0-1).