The Argentinian made it 37 goals in 24 Primera Division games this season as Barca came from behind to win 2-1.
The equaliser was a tap-in, with the winner a curling 25-yard free-kick.
Defender Jordi Alba said there are no words to describe Messi's achievements.
"Messi decided the match," he said on the Barcelona website. "301 goals for Messi, whatever anyone says will come up short."
Midfielder Sergio Busquets added: "He improves on a daily basis, he's the best in the world."
Dani Alves admitted playing alongside Messi made it easier for the other players. "Playing next to Messi gives you a lot of calm," he said. "It makes it easier to get things done."
Barca assistant coach Jordi Roura, still overseeing first-team affairs with head coach Tito Vilanova undergoing cancer treatment in New York, described his star player's latest feat as "incredible".
But Roura accept that his side did not have things all their own way at the Estadio Nuevo Los Carmenes and had to battle to earn the three points.
"We knew how difficult it is to win in this stadium," he said. "Granada are a very physical side and they had nothing to lose.
"The match became complicated (after they scored) and, once again, (my) players dug deep (to get the result).
"We fought back from behind and the fact that we won three important points makes us happy."