Two first-half penalties, from captain Andres Iniesta and Cesc Fabregas, set the champions on their way and Alexis Sanchez put the result beyond doubt 19 minutes from time - soon after the visitors had lost midfielder Manuel Iturra to a red card.
Pedro added a fourth in the final minute to complete the rout as Barca moved provisionally six points clear at the summit ahead of the rest of the weekend's action.
The Catalan club headed into the game decimated by injuries, with Victor Valdes, Dani Alves and Xavi having recently joined Lionel Messi, Jordi Alba, Jonathan Dos Santos, Ibrahim Afellay and Cristian Tello on the sidelines.
Fabregas and Gerard Pique returned after injury, though, and the home team always looked like they had too much for the eighth-placed visitors.
Alexis and Iniesta tried their luck from the edge of the box in the opening few minutes, but Granada goalkeeper Roberto was equal to both, while Neymar also lashed over the bar from 20 yards.
The best Granada could muster in the early stages was a couple of long-range efforts - from Youssef El Arabi and Piti - neither of which troubled Barca goalkeeper Jose Pinto.
The hosts took the lead in the 20th minute, Iniesta coolly placing his right-footed penalty into the bottom-right corner after the referee adjudged Fabregas had been fouled by Dimitri Foulquier.
Piti went within a whisker of snatching a swift equaliser, but saw his fierce left-footed shot hit the bar.
And before the break Gerardo Martino's side had doubled their advantage - again from the penalty spot. This time it was Iniesta who won it, when he was brought down by Fran Rico, and Fabregas who converted, despatching into the top-right corner of Roberto's net.
Granada could have pulled a goal back soon after the restart, but El Arabi directed his header over the bar.
The visitors' afternoon took a turn for the worse midway through the second half when Iturra was sent off for a second bookable offence following a foul on Pedro, having been yellow-carded in the first half for a challenge on Neymar.
Again they showed they should not be written off and forced a decent save out of Pinto soon after, the Barca keeper parrying a close-range attempt from Allan Nyom in the 70th minute.
However, the game was put beyond their reach moments later when Chile forward Alexis latched onto Neymar's slick pass and dinked over the advancing Roberto for his eighth goal in La Liga this term.
With the points in the bag, Barca boss Martino handed a first-team debut to 17-year-old Adama Traore in place of Neymar with seven minutes left.
And then, just to rub salt into the Granada wounds, Fabregas teed up Pedro for a fourth goal in the 90th minute.