On the second play from scrimmage, DeAndre Scott intercepted a Licata pass and returned it 37 yards for a touchdown, giving Akron a 7-0 lead just 23 seconds in.
Taylor lost a fumble on Buffalo's ensuing possession, but the Bulls forced a three-and-out.
On fourth-and-3, Johnson faked a run up the middle before hitting Matt Weiser with a jump-pass for a 33-yard touchdown, the first of 21-straight points for Buffalo.
Akron (4-6, 2-4) trailed by double-digits the rest of the way.
Interim coach Alex Wood, who replaced Jeff Quinn on Oct. 13, earned his first win at Buffalo.