Following a four-match winless run, Kgatlana put Eibar in front in the sixth minute following an assist from Mar Torras.
Tenerife, however, fought their way back when Pisco assisted Cristina Martin-Prieto to level in the 32nd minute before Noko Matlou bagged her second yellow on the brink of the half-time break.
After the restart, the 10-player visitors held on until Tenerife profited from their numerical advantage to claim the matchwinner through Martin-Prieto s second of the day eight minutes from full-time.
South Africa s Kgatlana was in action for the duration of the match and earned her ninth goal in 18 appearances, including five assists for Eibar.