In this paper, we employ the Truncated Painlevé Approach (TPA) to (2+1)-dimensional Maccari equation and construct its solutions in closed form involving three lower dimensional arbitrary functions that are completely separated in the spatial and temporal variables. We then suitably harness the arbitrary functions to generate localized solutions like dromions, rogue waves, stationary rogue waves, lumps, and compactons. The highlight of the results is that the localized solutions do not evolve in space and their amplitude alone changes with time despite possessing an explicit time dependence in their structure. Besides, they are also found to be noninteracting. © 2017 Elsevier B.V., All rights reserved.