Jelavic continued his fine build-up to the new Premier League campaign with an impressive first-half strike after good work by Mirallas to net his fourth goal of the summer.
Mirallas doubled the tally in freak circumstances as Betis goalkeeper Stephan Andersen fumbled the Belgian's corner into the net just after the hour.
Brian Rodriguez claimed a last-minute consolation for the Spanish side.
The downside for Everton and new manager Roberto Martinez was an injury to midfielder Darron Gibson, who limped off before half-time.
The Toffees are at Norwich for their Premier League opener next Saturday.