The victory has moved the Spanish champions into second position in the table, while winless Granada, who frustrated the home side for long spells of the contest, remain rooted to the bottom.
Injuries have robbed Barcelona of the likes of Andres Iniesta, Gerard Pique and Jordi Alba in recent weeks, but a strong XI at Camp Nou included Lionel Messi, Neymar and Luis Suarez as head coach Luis Enrique took no chances with his team selection against the struggling visitors.
It was actually quite a bright start from Granada, who twice broke through the Barcelona defence in the opening 10 minutes of action, but were denied by the offside flag on both occasions.
Barcelona were dominating in terms of possession as the first period continued to gather pace, but chances were few and far between as Granada frustrated Messi and Neymar with last-ditch clearances on more than one occasion. Indeed, 27 minutes passed at Camp Nou without a single opportunity of serious note.
Suarez had the home side's first clear opening in the 28th minute, but the Uruguay international was denied by a challenge from Ruben Vezo after attempting to round Granada's on-loan goalkeeper Guillermo Ochoa.
Suarez had another chance for Barcelona 10 minutes before the break after finding space outside the Granada box, but the striker's curling effort was pushed away by Ochoa as the visitors remained unbroken at the back.
The away side's best chance of the first period came on the counter attack when on-loan Manchester United midfielder Andreas Pereira released Artem Kravets, who the Spanish side have borrowed from Dynamo Kiev, but the striker just took the ball too wide and his strike towards goal was blocked.
Barcelona took the lead just three minutes into the second half when Rafinha produced a stunning overhead kick into the top corner after Neymar struck the post from close range following a slick move from the home side.
The champions failed to seriously grasp hold of the match, however, and Granada were a threat on the counter-attack with their willingness to leave players on the shoulder of what was a very high Barcelona defensive line.
Neymar had a chance to score Barcelona's second in the 63rd minute after meeting a deep cross from Sergi Roberto, but Ochoa was on hand to save as the Mexican kept the away side in the match.
On-loan Chelsea midfielder Jeremie Boga was introduced for Granada as head coach Lucas Alcaraz looked for fresh impetus in the final third and the Frenchman had a strike deflected wide of the Barcelona post by Javier Mascherano 25 minutes from time.
Suarez had a frustrating night at Camp Nou and headed his best chance of the match straight at Ochoa five minutes from time as Granada remained one goal behind the champions entering the latter stages of action.
Messi should have put the game to bed in the 89th minute when he broke into the away side's box, but the Argentine lifted the ball over the crossbar as Barcelona ran out narrow winners over a stern and impressive Granada outfit, who have now lost seven of their 10 La Liga matches this season.
Next up for Barcelona is a trip to Manchester City in the group stage of the Champions League on Tuesday night, before visiting in-form Sevilla in the league next Sunday. Granada, meanwhile, return to action at home to Deportivo La Coruna next Saturday.