Griezmann ended his goal drought of nine matches in all competitions as Barca closed the gap on the Madrid clubs at the top of the table.
Barca took the lead after 12 minutes when Griezmann reacted quickest inside the box and finished into the bottom corner.
Griezmann then turned provider when he set up Messi who curled the ball into the top corner.
Messi scored his second just before half-time with a stunning free-kick. The Barca captain has now scored 10 goals or more in La Liga for the 15th consecutive campaign.
Griezmann grabbed his second of the match after 63 minutes with a half-volley from a tight angle.