Manuel Pellegrini's side delivered another outstanding performance in Seville, with Isco scoring twice, while Abde Ezzalzouli, Diego Llorente and José Antonio Morante also found the net.
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The emphatic victory moved Betis to 19 points from eight matches, leaving them level with Atlético Madrid in second place.
Their remarkable start represents the club's highest points tally at this stage of a top-flight campaign, surpassing the previous record of 17 points established during the 1996/97 season.
With six victories, one draw and one defeat, Betis have also matched their opening eight-game record from the historic 1934/35 campaign, when they claimed the Spanish league title.