Betis were missing their top goalscorer Isco, who is out for several weeks with a thigh injury. But his absence was barely noticed as the visitors took the lead after five minutes.
Cardoso won the ball on the right flank and his cut back was swept home first time by Willian José.
Pablo Fornals made it 2-0 less than a minute into the second half when he curled a superb left-foot strike past the outstretched hand of Jeremias Ledesma.
Cardoso's assist capped another good performance since he signed from Brazilian club Internacional in January.
"Johnny had a good game," coach Manuel Pellegrini said.