The former Liverpool star, who netted twice in Wednesday's 2-1 UEFA Champions League triumph at Manchester City, scored his fourth goal in as many matches and had a hand in two more, ensuring Barca bounced back from their shock 1-0 defeat to Malaga last weekend.
Suarez played a crucial role in Barca's first, setting up Ivan Rakitic for an easy finish with just under half-an-hour played at Estadio Nuevo Los Carmenes.
And the pair switched roles at the start of the second half, as the Croatia playmaker teed up Suarez to open a two-goal lead.
Granada swiftly responded, as Fran Rico buried a 53rd-minute penalty, but the Catalans killed off any revival in the 70th minute, Lionel Messi tapping in for his 27th league goal of the season following more impressive play by Suarez.
The visitors had no problems holding on to their lead and they could have made the victory even more comfortable, but regardless of missing late chances, the triumph sees Barca move back to within a point of Real Madrid, who face Villarreal on Sunday.
Luis Enrique resisted the urge to rotate his key players in the wake of Barca's Champions League exploits in Manchester, with Messi, Neymar and Suarez all starting once again.
Suarez was somewhat fortunate not to see his game cut short in the 15th minute, though, as he caught Juan Cala in the face with a swing of his elbow.
And the forward ultimately proved integral as Barca opened the scoring 10 minutes later, playing the ball across the face of goal towards Rakitic, who could not miss after pouncing on a failed clearance by former Sevilla team-mate Cala.
Messi went close to doubling Barca's lead with 35 minutes on the clock, but after flicking the ball beyond a defender, the Argentina star smashed his half-volley agonisingly over.
Barca eventually added a second two minutes into the second half, as Suarez raced on to Rakitic's incisive pass and coolly poked the ball past Oier in the Granada goal.
The hosts received a boost to their chances a few moments later through Rico, though, as the midfielder converted from the spot following a foul by Marc Bartra on Lass Bangoura.
But any fight-back from the hosts was quashed 20 minutes from time.
Suarez was at the fore once again, chasing down a long ball and racing beyond Oier, before providing Messi with a simple finish instead of knocking into an unguarded net himself.
Barca could have added more in the final 10 minutes as Messi went close twice, but the missed opportunities ultimately had no effect, with the away side cruising to a straightforward win.
