Four minutes later, Raquel Pinel doubled the hosts' lead with her brilliant individual finish before Pina set up Payne to increase the advantage to three, four minutes from half-time.
However, the visitors came out strong in the second half and pulled one back when Cristina Martinez teed up Ainoa Campo to score five minutes after the break, but her effort could not save them from defeat.
Nigeria's Payne featured for the duration of the game and grabbed her fourth league goal of the season in 29 outings for Sevilla.
Namibia's Zenatha Coleman came on as a late second-half substitute, replacing Pina five minutes from full-time.