First-half penalties from Andres Iniesta and Cesc Fabregas put the Catalans in command at the break.
Granada were then left to play the final quarter of the game with 10 men as Manuel Iturra was shown a second yellow card.
Alexis Sanchez added a third soon after from Neymar’s pass before Pedro Rodriguez rounded off the scoring a minute from time.
Barca’s title rivals Real Madrid and Atletico Madrid can close the gap later on Saturday as they face Almeria and Getafe respectively.
With Victor Valdes, Xavi Hernandez, Dani Alves and Jordi Alba also out injured, Barca boss Gerardo Martino was forced into making seven changes from the side that started their last outing against Real Betis two weeks ago.
In Messi’s absence, Neymar was tasked with playing in the false nine role, but it was from a free-kick that he nearly created the opener as he picked out Sanchez and Granada keeper Roberto made a brilliant save to turn away the Chilean’s flicked header.
The opener arrived after 20 minutes when Dimitri Foulquier brought down Fabregas and captain for the day Iniesta took responsibility to slot the spot-kick low into the corner of the net.
Granada came close to an equaliser four minutes later with their best effort of the game as Piti drilled a shot from 25 yards off the crossbar.
Foulquier then made amends for conceding the penalty with a fine last-ditch tackle to prevent Sanchez making it 2-0 from Fabregas’ fine pass.
However, it didn’t take long for Barca to double their advantage as Fran Rico clipped Iniesta’s heels just inside the area and this time Fabregas stepped up to rifle the ball into the roof of he net.
Youssef El-Arabi had a chance to halve the deficit from Yacine Brahimi’s cross two minutes after the restart, but he headed wastefully.
It should have been three for Barca moments later when Pedro somehow blazed over when presented with an open goal after Roberto had flapped at Martin Montoya’s cross.
The visitors’ task became even tougher 23 minutes from time when Iturra saw his second yellow card for upending Pedro.
Sanchez made it 3-0 when he lifted the ball over the advancing Roberto from Neymar’s well-weighted through ball five minutes later.
With the game won 17-year-old Adama Traore replaced Neymar to make his Barca debut and he nearly sealed it with a memorable goal as he weaved past three Granada defenders before Roberto smothered his low effort.
And Pedro put the shine on another comfortable afternoon for the Spanish champions when he turned home Fabregas’ cross.