This paper proposes a robust control strategy for the synchronization of parallel connected single-phase inverters through sliding mode-controlled harmonic oscillators. Synchronization is achieved through two non-linear sliding surfaces and, in finite time (less than 2 AC cycles), invariant to initial conditions and parameter perturbations. High-quality synchronization and robustness to uncertainties enable the inverters to operate in grid-forming mode too. The proposed control strategy generates perfect sinusoidal response at the output of inverters, i.e., lower levels of total harmonic distortion (THD) are achieved, which helps in maintaining the power quality of the electrical grid. The analytical results are validated by simulation case studies.