The Uruguay striker scored Barca's opener with a classy lob in the 44th minute and provided assists for Paco Alcacer and Ivan Rakitic to seal the points after the home side surprisingly drew level early in the second half through Jeremie Boga.
Neymar added extra shine to the victory with his 100th goal for Barca by knocking in a cross from Alcacer in added time.
Barca are second on 66 points, two behind Real Madrid who beat Alaves 3-0 earlier on Sunday and have a game in hand.
La Liga top scorer Messi was suspended for Barca's trip to the picturesque Andalusian city, where they clinched the title last season, and coach Luis Enrique took a risk by resting regulars Gerard Pique, Andres Iniesta and Samuel Umtiti before losing Rafinha to injury in the 17th minute.
The visitors dominated but took 44 minutes to open the scoring when Suarez calmly chipped Jordi Alba's sumptuous through ball over goalkeeper Guillermo Ochoa to finally get the better of the Mexican.
Boga grabbed an equaliser five minutes after the break for second-bottom Granada and Luis Enrique's rotations suddenly looked misguided before Suarez got them out of jail.
He teed up Alcacer in the 64th and then provided a pass to Rakitic which was deflected in off Matthieu Saunier just after Granada's Uche Agbo was sent off for a second booking.
Neymar rounded off the victory with his milestone goal.
(Reporting by Richard Martin; Editing by Ken Ferris)
Share
