One of the event shape observables, the transverse spherocity ($S_0$), has been studied successfully in small collision systems such as proton-proton collisions at the LHC as a tool to separate jetty and isotropic events. It has unique capability to distinguish events based on their geometrical shapes. In our work, we report the first implementation of transverse spherocity in heavy-ion collisions using a multi-phase transport model (AMPT). We have performed an extensive study of azimuthal anisotropy of charged particles produced in heavy-ion collisions as a function of transverse spherocity ($S_0$). We have followed the two-particle correlation (2PC) method to estimate the elliptic flow ($v_2$) in different centrality classes in Pb-Pb collisions at $\sqrt{s_{\rm NN}}= 5.02$~TeV for high-$S_0$, $S_0$-integrated and low-$S_0$ events. We found that transverse spherocity successfully differentiates heavy-ion collisions’ event topology based on their geometrical shapes i.e. high and low values of spherocity. The high-$S_0$ events are found to have nearly zero elliptic flow while the low-$S_0$ events contribute significantly to elliptic flow of spherocity-integrated events.