Messi scored twice in the first period at Camp Nou, before adding his third just before the hour as the Catalan outfit moved one point clear of Atletico Madrid at the summit. Granada improved in the second period after struggling in the first, but it got worse late on when Neymar made it four in the 83rd minute.
Jordi Alba then had the ball in the back of the net for Barcelona, but the left-back was just offside when Messi slid a pass into the path of the Spanish international, before Luis Suarez brought a smart stop from Andres Fernandez all inside the opening seven minutes.
In the eighth minute, Barcelona took the lead as Messi converted form close range after an Arda Turan pass. There was a hint of offside about the goal, but the flag stayed down and Turan had an assist to his name on his La Liga debut for the Catalan outfit.
Turan came close to a goal of his own in the 14th minute, but the Turkish international, who was through on goal, was denied by a last-ditch challenge from Doria. Less than one minute later, however, Barcelona had their second of the match when Messi converted from a tight angle after a low cross from Suarez.
Suarez had Barcelona's next outstanding chance in the 27th minute, but after combining with Neymar, the Uruguay international somehow fired wide of the post from inside the box. Messi then found space inside the box, but Fernandez managed to make a point-blank save to keep out the Argentine.
Neymar also came close to adding to the scoring in the latter stages of the first period, but Granada, whose best outlet came from Isaac Success, managed to keep the score down with a couple of clearances from Doria.
Success remained Granada's biggest threat early in the second half and after cutting inside Alba, the attacker released a strike from distance, but Claudio Bravo was on hand to make the save, before David Lomban tested the Barcelona stopper with a powerful free kick from just outside the box.
Messi completed his hat-trick just before the hour, however, when he tapped home from close range after Neymar had struck the post with a low effort.
Rochina came close to a consolation for Granada in the 67th minute, but after turning inside the Barcelona box, his effort was kept out by Bravo. Chances proved few and far between in the 15 minutes that followed, with substitutions from both managers making it a stop-start period of the contest.
Barcelona were not finished, however, and added a fourth through Neymar in the 83rd minute to cap what was a miserable afternoon for relegation-threatened Granada.