Suarez was suspended for two games in that competition, pending an appeal, for trying to provoke opponents in the tunnel, while Dani Alves is in hot water for speaking out against the media.
Luis Enrique chose to give the Brazilian a rest, handing Aleix Vidal a start at right-back and also keeping Arda Turan in the side.
The pair made their debuts in the Copa del Rey in midweek, but this was their first La Liga start.
The Blaugrana boss rang the changes ahead of what is sure to be draining second leg of their cup tie against Espanyol on Wednesday, with Andres Iniesta, Sergio Busquets and Javier Mascherano also benched, with the latter cut from the squad entirely. It made no difference to the team’s chances of success.
Jordi Alba spurned a chance to take what should have been the opening goal after just four minutes, played in by Messi but firing too close to Andres Fernandez.
But in the 8th minute, Barcelona struck. Messi passed the ball out to the left, where Suarez dummied it and Arda collected it behind him, nutmegging the covering defender with a low pass which Messi brushed home.
The second goal came sooner, rather than later, with Neymar breaking down the left, looping a ball to Suarez on the right, who crossed it back to the left, where Messi was left to tap into an empty net.
Following that Barcelona created chances but lazily spurned most of them. Neymar played in Suarez, who rounded the goalkeeper but fired wide. The Uruguayan lay down on the turf and laughed.
Messi should have had his hat-trick after 32 minutes but when Vidal surged round the defence and cut it back, the Argentine’s shot was weak and straight at Andres.
Neymar then hit the side-netting with a searing volley from Ivan Rakitic’s pass, before juggling the ball on the edge of the box and chipping one a yard over the top corner of Granada’s goal.
Messi struck again in the second half after Neymar’s strike rebounded back off the post, before the Brazilian got on the scoresheet himself as the game entered its final stretch.
This was another goal concocted by the trident, with Messi feeding Suarez, who raked a low ball to the far post where Neymar was waiting. One touch to control it, another to launch it into the roof of the net from about four yards out. Emphatic. And scary, considering Barcelona barely got out of third gear.
It will be more trouble for Messi to concoct his Ballon d’Or acceptance speech than it was for him to dismantle Granada at the Nou Camp.