The Catalan giants entered week 38 leading second-placed Real Madrid by one point and knowing that a win would secure a 24th La Liga crown and make it back-to-back championships after wrestling the crown from Atletico Madrid last season.
As it transpired, Real Madrid beat Deportivo La Coruna 2-0 in their final match, but a comfortable afternoon for Barcelona saw Luis Enrique's side hold off pressure from the Bernabeu to finish top of the pile.
Barcelona had a golden chance to take the lead in the seventh minute when Javier Mascherano's flicked header found Gerard Pique inside the box, but the Spaniard could not beat Granada stopper Andres Fernandez from close range.
Fernandez was again called into action in the 10th minute when Lionel Messi struck one from distance, but the goalkeeper was equal to the effort as the home side managed to keep out Enrique's side in the early exchanges.
Two minutes later, a Messi pass found Neymar inside the home side's box, but David Lomban was across to make a last-ditch challenge, before Pique headed the resulting corner straight into the arms of the busy Fernandez.
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Barcelona finally made the breakthrough in the 22nd minute when Jordi Alba beat the offside trap and fed a low cross into Suarez, who could not pass up the chance to score his 38th La Liga goal of the season.
Meanwhile, Cristiano Ronaldo had scored twice to leave Real Madrid 2-0 ahead at Deportivo, making Suarez's breakthrough strike even more important for the league leaders entering the final matchday of the season.
The visitors continued to dominate matters in the first period and they had their second of the match in the 38th minute when Dani Alves delivered a cross into Suarez, who headed past Fernandez after reacting quicker inside the box.
Granada failed to register a single shot on target in the first 45 minutes of action and at the interval, Barcelona were comfortably heading for all three points and a 24th top-flight Spanish title.
Barcelona's dominance continued early in the second period as Ivan Rakitic twice set up half-chances for Suarez and Pique, but neither could score the game's third goal, which would have certainly made sure of the points.
Messi tried his luck from a free kick in the 55th minute as the visitors continued to threaten, but Fernandez was on hand to make a smart save, before Marc-Andre ter Stegen kept out Fran Rico down the other end in Granada's first attempt on goal.
Neymar was next to come close for Barcelona after Suarez found his fellow South American just past the hour, but Fernandez was on hand to make the save and keep his team in the match.
Granada did improve in the second half and Jean-Sylvain Babin sent a header over the crossbar in the 67th minute during what was an end-to-end period of the contest in Andalusia.
A series of yellow cards and substitutions slowed the play entering the final 15 minutes and although Granada had more attacking intent in the second period, it proved to be an extremely comfortable afternoon for Enrique's side, who scored their third in the 86th minute when Neymar set up Suarez for the Uruguay international's hat-trick.
Barcelona lost three successive La Liga games in April to throw the title race wide open and despite Real Madrid winning their last 12 games of the season, it was the Catalan outfit that secured the crown once again.
Barcelona, who have taken the title by one point from second-placed Real Madrid, will go in search of a domestic double when they face Sevilla in the Copa del Rey final next weekend.