The Toffees prepared for their clash with Norwich on August 17 with an impressive victory, with Brian Rodriguez grabbing a consolation goal late on for the visitors
Martinez's men wrapped up the win courtesy of goals from attackers Nikica Jelavic and Kevin Mirallas, with Brian Rodriguez's late goal little more than a consolation for the Spanish side.
Former Wigan boss Martinez named a strong starting line-up with Leighton Baines, Leon Osman and Steven Pienaar all featuring.
However, it was Betis who created the better chances in the early stages, striker Jorge Molina and midfielder Javier Matilla both going close in the first 30 minutes.
Pepe Mel's side did not seize their opportunities, though, and Everton took the lead 10 minutes before the break with their first notable attack of the game.
Jelavic slotted home with a composed finish from close range after the visitors failed to clear Mirallas' right-wing cross.
Still, Tim Howard continued to be the busier of the two goalkeepers, producing good saves to deny Nosa Igiebor and Molina and keep Everton - who saw Darron Gibson limp off just before half-time - in front until the interval.
Betis pressed for the equaliser in the opening stages of the second half as Igiebor and Molina both wasted opportunities to equalise, before Howard saved with his face to prevent the latter from levelling the scores.
Again Mel's men were punished for their profligacy, as Mirallas doubled Everton's lead in bizarre fashion as goalkeeper Stephan Andersen dropped the Belgium international's corner kick into his own net after 65 minutes.
Jelavic and Mirallas combined shortly after as Everton searched for a third, but the Croatian skewed a shot wide at the end of a fine move.
Mirallas also went close to doubling his tally as he whipped a free-kick just over the bar, but it was Betis who had the final say, with Rodriguez finding the net after a scramble in the Everton box.