Messi scored twice and set up another goal, dominating proceedings, while Suarez added three of his own after Arda Turan's opener.
Ruben Castro struck a brace for Betis but at no stage of the game did it seem like the visitors had enough to prevent Luis Enrique's team from running amok on the opening day of the new Spanish season.
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Asked if he was surprised about Messi hitting the ground running this season after the trauma of losing the Copa America final with Argentina, Luis Enrique replied: "No, no. He's Lionel Messi. He's always the same.
"If he and Luis [Suarez] get involved with the rest of the team, you can only say that they enjoy it."
Betis coach Gus Poyet admitted he wished Messi hadn't been so brutally effective against his team. "As a football fan, I enjoyed Messi. Playing against him, you don't want him to do so well. Messi's goal destabilised us and from there it is complicated to play football here," he said. "If you want to go and win the game they will score five or six against you. It happens a lot here.
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"As a team or a group we have to be mentally strong to continue in the same way, confident in all the aspects of our play."
New signings Samuel Umtiti and Denis Suarez started for Barcelona, standing in for Javier Mascherano and Andres Iniesta respectively, as Barcelona battled with a long list of absences.
Former Athletico Madrid midfielder Turan, who was the star performer in the Spanish Super Cup second-leg tie against Sevilla, was once again on a scoring sheet.
The 29-year-old has already surpassed his total goal tally of the last season, which means he is settling at the club after a turbulent first season with the Catalans.
In other matches, Villarreal drew 1-1 at Granada, while Sevilla beat Espanyol 6-4 in an incredible game.
Barcelona’s biggest rivals Real Madrid will face Real Sociedad on Sunday evening, whereas Atletico Madrid will also entertain promoted Alaves later in the day.
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