Cross sections were determined by the activation technique for the reactions 64Zn(p,γ)65Ga, 66Zn(p,γ) 67Ga, and 67Zn(p,γ)68Ga in the center of mass energy range between 1 and 3 MeV using the proton beam of the Van de Graaff accelerator at KIPT, Kharkiv. Thin enriched targets of zinc isotopes on thick tantalum backings were used in the experiment. The radioactivities of 65Ga, 67Ga, and 68Ga were measured by high-resolution γ-ray spectrometry. S-factors and reaction rates were derived from the experimental cross sections and compared with the statistical theory predictions using the new computer code NON-SMOKERWEB. Despite the largely different magnitudes of the cross sections of the first two reactions, theory reproduces the experimental values equally well. Best agreement of the predictions with the experimental data was achieved with a modification of the optical model potential and variation of radiative widths The sensitivity of the results on different theory parameters is studied. This is an important test of the model for proton capture at energies relevant in p-process nucleosynthesis.