Mechanisms controlling fracture permeability enhancement during injection-induced and natural dynamic stressing remain unresolved. We explore pressure-driven permeability (k) evolution by step-increasing fluid pressure (p) on near-critically stressed laboratory fractures in shale and schist as representative of faults in sedimentary reservoirs/seals and basement rocks. Fluid is pulsed through the fracture with successively incremented pressure to first examine sub-reactivation permeability response that then progresses through fracture reactivation. Transient pore pressure pulses result in a permeability increase that persists even after the return of spiked pore pressure to the null background level. We show that fracture sealing is systematically reversible with the perturbing pressure pulses and pressure-driven permeability enhancement is eminently reproducible even absent shear slip and in the very short term (order of minutes). These characteristics of the observed fracture sealing following a pressure perturbation appear similar to those of the response by rate-and-state frictional healing upon stress/velocity perturbations. Dynamic permeability increase scales with the pore pressure magnitude and fracture sealing controls the following per-pulse permeability increase, both in the absence and presence of reactivation. However, initiation of the injection-induced reactivation results in a significant increase in the rate of permeability enhancement (dk/dp). These results demonstrate the role of frictional healing and sealing of fractures at interplay with other probable processes in pore pressure-driven permeability stimulation, such as particle mobilization