This study describes the discovery of a phase separation phenomenon in supercritical fluids (SCFs). An SCF is technically a single-phase fluid with two sub-domains separated by the Widom line. A pseudo phase transition occurs between liquid-like (LL) and gas-like (GL) states, similar to the gas-liquid phase transition across the coexistence line in subcritical fluids. By extending the analogy, we demonstrate that LL-GL phase separation is possible by generating submicron size LL argon droplets in a GL argon SCF. The GL fluid is in a quasi-equilibrium clustered state well above the critical temperature, with a significant increase in cluster formation rate traversing the critical pressure. The prolonged phase separation over an hour is consistent with a model of mass transport mediated by clusters. It provides the insight that clustering is an essential factor in transport and non-equilibrium thermodynamic processes in SCFs.