We report room temperature lasing in ZnO inverse opal photonic crystals in the near-ultraviolet (UV) frequency range. We observe random lasing due to disorder in the structures when the photonic pseudogaps are located away from the ZnO gain spectrum. Tuning the first ΓL-pseudogap to the gain peak leads to a five-fold reduction in lasing threshold and a frequency shift of the lasing modes due to the enhanced confinement of light.