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.
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.
Along with his two strikes against Sevilla that sealed Barcelona's Spanish Super Cup win last week, the goal meant he has already scored more this season than he did in his disappointing debut campaign with Barcelona.
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While Turan is starting to come to life in a Barca shirt, goalkeeper Claudio Bravo is set to end his time at the Camp Nou, with a move to Manchester City reported to be close.
The hosts reacted instantly. Turan had a half-chance to restore Barcelona's lead but couldn't direct Sergi Roberto's raking low cross on target, before Denis Suarez had a strike deflected over and Messi cracked a strike against the crossbar.
Eventually Messi put them back ahead with a thunderbolt from outside the box. As he shaped to shoot everybody in the stadium knew what was coming, but there was still nothing goalkeeper Antonio Adan could do to stop it as the Argentine lashed home.
Barcelona continued to pile on the pressure in the second period, with Messi twice foiled by Adan, while Denis Suarez had a strike saved too and the assistant referee's flag stopped Turan from adding to his tally after he bundled home from close range.
Then came two goals in quick succession, Messi setting up Luis Suarez for a tap-in, before driving home his second and Barcelona's fifth from outside the area again.
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