First-half penalties from Iniesta and Fabregas were added to by Sanchez in the 71st minute and Pedro a minute from time at Camp Nou, while the closest the visitors came was when Piti thundered a shot off the crossbar with the score still at 1-0.
Barcelona made light of being without the injured duo of Lionel Messi and Victor Valdes, Iniesta opening the scoring in the 20th minute following a foul on Fabregas, before the roles were reversed 20 minutes later.
In the second half, Neymar played in Sanchez and Fabregas teed up Pedro to put the seal on another comfortable win for Gerardo Martino's side.
Barca's victory was their fifth in succession and their 13th in 14 overall in La Liga, while the setback for Granada came as a blow after winning three of their past four matches.
The hosts went close in the 14th minute as Roberto reacted smartly to parry Neymar's free-kick from the left.
Jose Pinto, called in as replacement for Valdes, held Piti's 25-yard free-kick on the half-hour mark, before Barca doubled their lead five minutes before the break, again from the penalty spot.
Allan Nyom should have halved the deficit moments before Barca's third, drilling the ball straight at Pinto from close range before the hosts broke at speed, Neymar sliding a pass for Sanchez to finish with a minimum of fuss.
