A subsurface safety valve includes an interior bore and a hinged valve actuatable between an open position and a closed position in which the hinged valve creates a fluid-tight seal with the interior bore. A latching mechanism secures an isolation tool within the interior bore of the valve. The isolation tool includes a tubular body having an exterior surface corresponding to the interior bore and an interior surface defining an internal bore. An annular groove is disposed on the exterior surface of the tubular body, and an annular seal is disposed in the annular groove. An equalization port is disposed downhole of the annular seal, and has one or more apertures for fluidly coupling an upper and lower portion of a wellbore. The subsurface safety valve further includes a control line for controlling the valve at a surface of the wellbore.