By defining dijet rapidity gap events according to interjet energy flow, we treat the photoproduction cross section of two high transverse momentum jets with a large intermediate rapidity region as a factorizable quantity in perturbative QCD. We show that logarithms of soft gluon energy in the interjet region can be resummed to all orders in perturbation theory. The resummed cross section depends on the eigenvalues of a set of soft anomalous dimension matrices, specific to each underlying partonic process, and on the decomposition of the scattering according to the possible patterns of hard color flow. We present a detailed discussion of both. Finally, we evaluate numerically the gap cross section and gap fraction and compare the results with ZEUS data. In the limit of low gap energy, good agreement with experiment is obtained.