Following a four-match winless run, Sevilla made a bright start to halt her disappointing form, although only gain the lead when Claudia Pina set up Carla Armengol to score on the brink of half time.
After the restart, the visitors continued their dominance as Pina bagged her second assist of the contest, teeing up Nigerian-born American Payne to double the lead in the 51st minute.
Eibar, however, fought for a comeback but only found a breakthrough when Kgatlana blasted past goalkeeper Noelia Ramos off a quick one-two with Maria Llompart 10 minutes from regulation time.
The comeback dreams of the hosts were dashed when Pina s hat-trick of assists aided late substitute Maite Albarran to guarantee the away victory for the visitors inside additional time.