The Spanish champions have dropped only two points so far this term.
The Uruguay international came off the bench to complete the rout of Granada.
Messi let his football do the talking on Sunday night.
Sergio Ramos’ penalty capped a comeback from 2-1 down after Betis’ Emerson scored an own goal and was sent off.
Betis, managed by former Los Blancos boss Manuel Pellegrini, had lead at half-time.
The Uruguayan has moved to Barca’s LaLiga rivals.
The striker is heading to Atletico Madrid.
Suarez won four LaLiga titles, four Copa del Reys and the Champions League in six seasons with Barca.
The Spanish champions won 10 successive matches towards the end of last season to secure the title
The club confirmed on Saturday that Messi, Sergio Busquets, Gerard Pique and Sergi Roberto will remain as the club’s top four options for the armband.