We show that due to near-field interaction of plasmonic particles via gain particles, a two-dimensional array of incoherently pumped spasers can be self-synchronized so that the dipole moments of all the plasmonic particles oscillate in phase and in parallel to the array plane. The synchronized state is established as a result of competition with the other possible modes having different wavenumbers and it is not destroyed by radiation of leaking waves, retardation effects, and small disorder. Such an array produces a narrow beam of coherent light due to continuous-wave superradiance. Thus, spasers, which mainly generate near-fields, become an efficient source of far-field radiation when the interaction between them is sufficiently strong.