The home side were ahead after just a minute when Jose Antonio Reyes took full advantage of a poor goalkeeping error to produce a composed finish from close range.
Betis were two goals behind just five minutes later when defender Fazio rose highest in the area to thump an emphatic header home and send the home fans wild.
Things went from bad to worse for the visitors when Reyes doubled his tally before the break after pouncing on some slack defending.
Sevilla were four goals to the good just minutes later as Fazio met a precise Reyes cross to bag a brace of his own.
Betis were reduced to ten men early into the second half when Ruben Perez recieved a second yellow card after batting the ball away with his hand.
Sevilla conceded a consolation with twenty minutes to play, leaving Ruben Castro unmarked to smash home at the back post.
A comedy of errors in the Betis backline gave the scoreline some added gloss in stoppage time as Ivan Rakitic curled home unchallenged after a swift Sevilla counter created by the influential Jesus Navas.