Having ended 2020 with a 4-2 defeat at Valencia, Iker Dorronsoro handed the South Africa duo starting roles against compatriot Nothando Vilakazi, who came on from the bench for the visitors.
Kgatlana got the assist for the opener when she set up Kuki to open the scoring after 33 minutes of action.
Eibar continued from where they left off in the second half as Kuki provided an assist for Arola Aparicio to wrap up the victory two minutes after the restart at the Unbe Sports Complex.
Kgatlana has now grabbed five assists and five goals in 12 outings this season, lasting 83 minutes before making way for Aida Esteve, while compatriot Matlou featured for the duration on her debut.
Logrono continued their dominance in the encounter and found another breakthrough five minutes later through Valeria Pascuet.
Five minutes from the half-time break, the Ghanaian midfielder found herself in a good position and notched her second of the match for the hosts after firing past goalkeeper Andrea De la Nava.
Asantewaa, who was in action for 82 minutes before being replaced by Lorena Valderas, has now scored two goals in 12 appearances for Gerardo Leon s team this season.
Equatorial Guinea s Boho and Cote d Ivoire s Rebecca Elloh were involved for the duration but South Africa s Nothando Vilakazi only lasted for 27 minutes on her second start for Logrono.
With Betis without a win in six games, Gerardo Leon s side were eager to end their poor run against the fellow strugglers and Guehai got them off to a fine start with the opener after just two minutes.
On their return from recess, the visitors consolidated on their narrow first-half lead when Julie Tavlo-Petersson doubled the advantage, with her fine finish within just four minutes into the second stanza.
In the 82nd minute, Boho extended the visitors lead from the spot before they were reduced to 10-players following the sending off of their goalkeeper Pamela Tajonar three minutes later.
Real Betis, however, secured a consolation on the brink of full time when Rosa Marquez set up Aixa Garcia to score but could not deny Logrono s first win of the season at Polideportivo Felipe del Valle.