Two spot-kicks from Andres Iniesta and Cesc Fabregas had the Blaugrana well on their way before Alexis Sanchez and Pedro sealed a fifth league win in a row
First-half penalties from Andres Iniesta and Cesc Fabregas had Barca on cruise control before Lucas Alcaraz's men were reduced to 10 men following Manuel Iturra's second yellow card early in the second half.
The Blaugrana took advantage of the extra man when Alexis Sanchez struck in the 71st minute and Pedro completed the rout a minute from time at Camp Nou, making light work of Messi's enforced absence.
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.
Barcelona made six changes from the 4-1 win over Betis a fortnight ago with Messi (hamstring) and Valdes (calf) among a host of absentees for Martino, while Granada showed three alterations from their 3-1 win over Malaga.
The hosts went close in the 14th minute as Roberto reacted smartly to parry Neymar's free-kick from the left.
But Barca did not have to wait long for the breakthrough as six minutes later Fabregas was brought down in the box by Dimitri Foulquier and Iniesta stepped up to plant the subsequent spot-kick into the bottom right-hand corner.
Granada almost responded in spectacular fashion four minutes later, Piti driving forward and unleashing a thunderous effort from 25 yards that cannoned off the crossbar and behind to safety.
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.
Fran Rico brought down Iniesta as he prepared to shoot and this time Fabregas took responsibility, burying his spot-kick high into the top left-hand corner.
Five minutes into the second half, Pedro wasted a glorious chance to put the result beyond doubt, blazing the ball over from 10 yards with the goal gaping after Roberto had palmed a low cross into his path.
But the Barca winger would continue to frustate the visitors and his run was abruptly halted by Iturra just after the hour mark, which earned the midfielder a second yellow having already been booked in the first half.
Despite being reduced to 10 Granada's Allan Nyom should have halved the deficit moments before Barca's third, drilling the ball straight at Pinto from close range.
And it was to prove costly as the hosts broke at speed with Neymar sliding a pass for Alexis to finish with minimum fuss.
In the final minute, Fabregas countered down the left and squared for Pedro, who slid in to convert from eight yards to cap another impressive Barcelona performance.