Most organisms grow in space, whether they are viruses spreading within a host tissue or invasive species colonizing a new continent. Evolution typically selects for higher expansion rates during spatial growth, but it has been suggested that slower expanders can take over under certain conditions. Here, we report an experimental observation of such population dynamics. We demonstrate that mutants that grow slower in isolation nevertheless win in competition, not only when the two types are intermixed, but also when they are spatially segregated into sectors. The latter was thought to be impossible because previous studies focused exclusively on the global competitions mediated by expansion velocities, but overlooked the local competitions at sector boundaries. Local competition, however, can enhance the velocity of either type at the sector boundary and thus alter expansion dynamics. We developed a theory that accounts for both local and global competitions and describes all possible sector shapes. In particular, the theory predicted that a slower on its own, but more competitive, mutant forms a dented V-shaped sector as it takes over the expansion front. Such sectors were indeed observed experimentally, and their shapes matched quantitatively with the theory. In simulations, we further explored several mechanisms that could provide slow expanders with a local competitive advantage and showed that they are all well-described by our theory. Taken together, our results shed light on previously unexplored outcomes of spatial competition and establish a universal framework to understand evolutionary and ecological dynamics in expanding populations.