The victory ensured the host nation finished runners-up with five points and advanced two points adrift of group winners Congo, who edged Burkina Faso 2-1.
Having soaked up incessant pressure throughout the match, Equatorial Guinea took the lead against the run of play after forward Javier Balboa was fouled and then blasted home the spot-kick in the 55th minute.
Salvador rounded off a swift break in the closing stages, sweeping home a rebound after Gabon keeper Didier Ovono parried an Emilio Nsue shot straight into his path.
Equatorial Guinea goalkeeper Felipe Ovono was central to their success, having produced a string of superb saves to deny Gabon forwards Pierre-Emerick Aubameyang and Frederic Bulot.