Neymar opened the scoring with a composed
Luis Enrique's side dominated their lowly opponents, Suarez's acrobatic finish the highlight of a clinical team performance.
They have scored 14 goals in the past three games, while Messi looks to be nearing the form which saw him score 43 goals to help Barcelona to the La Liga title last season.
Barca have 33 points from 13 games.
Third-placed Real Madrid, who were hammered 4-0 by Barca last weekend and are now nine points off the pace, play Eibar on Sunday.
Barca's win took them seven points clear of nearest rivals Atletico Madrid, who later reduced the deficit back to four with a 1-0 win over Espanyol thanks to Antoine Griezmann's goal.