Griezmann opened the scoring early on and then set up Messi for Barca's second in the 35th minute. Messi added the third before the break from a free kick and Griezmann completed the scoring just after the hour mark.
Granada had Jesus Vallejo sent off late on for a last-man challenge on substitute Martin Braithwaite as Barca returned to third in the table, four points behind leaders Atletico Madrid, who have three games in hand.
The big positive at the start of 2021 is that Messi appears to have found his shooting boots. His performances have been good under new coach Ronald Koeman but he wasn't scoring as often as he usually does. That has changed in the last week, with back-to-back braces taking him to 11 goals for the season, more than anyone else in La Liga.
Two goals for the oft-criticised Griezmann -- both brilliant finishes -- were also much needed.
Perhaps for the first time this season, following three away wins in a week, Koeman's side look comfortable in a 4-3-3 system and the players seem aware of what they need to be doing to benefit the team.
Manager rating out of 10
7 -- Koeman, through luck or judgment, has stumbled upon his best side. A midfield three of Sergio Busquets, Frenkie de Jong and Pedri has helped Barca run into their best form of the season. Further forward, the width of Ousmane Dembele helps. The Dutch coach was even wise enough to take Messi off after the fourth goal, giving him a break ahead of next week's Spanish Super Cup.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Marc-Andre ter Stegen, 7 -- Made a great early save from Antonio Puertas when the score was still goalless and another from the same player later, although the flag did eventually go up for offsides.
DF Sergino Dest, 6 -- Recovered from an early injury scare to help Barca keep their second clean sheet in their last four games.
DF Oscar Mingueza, 7 -- A good performance from the youngster, stepping forward to win the ball and feed passes through the lines.
DF Samuel Umtiti, 6 -- Came into the side at the last minute after the injury to Araujo and did well on his first start of the season.
DF Jordi Alba, 6 -- Got forward a lot, as ever, but the glory in the final third went to other players on Saturday.
MF Sergio Busquets, 7 -- If not his best performance of the season, he certainly produced some of his best moments, be that long-distance passes or turning out of danger on the edge of his own box.
MF Frenkie de Jong, 7 -- Continued his good start to 2021 with another confident performance. Caused problems driving forward with the ball and played some good passes.
MF Pedri, 7 -- Not as impressive as he was at Athletic Bilbao in midweek but didn't need to be. Still intelligent with the ball, a threat when running with it and won the free kick that Messi scored.
FW Ousmane Dembele, 7 -- Like Pedri, a quieter performance than in recent weeks but was still good. Set up Griezmann's second goal with a nice lofted pass.
FW Lionel Messi, 9 -- Two great finishes helped Barca wrap up the three points before half-time. Smiling again and that may be the best news for Koeman's side.
FW Antoine Griezmann, 9 -- Needed a performance like this. Turned and finished really well for his first goal but his second was the best, a brilliant touch and strike from a right angle.
FW Martin Braithwaite, 6 -- Came on for Messi and provoked the challenge that saw Vallejo sent off.
MF Miralem Pjanic, 6 -- With Messi off, he took on free-kick responsibilities and had one great chance but hit the wall.
MF Riqui Puig, N/R -- Lovely pass freed Braithwaite in the lead up to Vallejo's dismissal.
FW Francisco Trincao, N/R -- Came on too late in the game to make an impression.
DF Junior Firpo, N/R -- Created a good chance for Braithwaite late on.