Luis Enrique's men were stunned 2-1 by newly-promoted Alaves at the Nou Camp in LaLiga on Saturday, but made amends by recording their biggest Champions League victory.
Aside from Messi's sixth career treble in the competition, Neymar and Andres Iniesta were also on the scoresheet with fine second-half strikes before Luis Suarez wrapped things with two more goals late on.
It might have been a different story had Moussa Dembele - hat-trick hero in Celtic's 5-1 derby mauling of Rangers at the weekend - not seen his 24th-minute penalty saved by Marc-Andre ter Stegen when it was 1-0, but the Scottish champions were convincingly beaten in the end.
Enrique stated: “Messi plays with complete freedom to change his position as he wants. He's the best in the world in every position.
“If he plays as a No 9, a No 8 or a No 6, he's the best No 9, No 8 or No 6 in the world. He can judge the perfect pass from 40 yards and put the ball wherever he wants. For me, he's the best player of all time."