Barca came into the clash on the back of a hard-fought 2-1 win over Real Sociedad over the weekend.
The visitors carved out the game's first opening after 11 minutes, but Gaston Pereiro's strike from the edge of the box sailed over the crossbar.
Ernesto Valverde's charges eventually took the lead in the 31st minute as Messi found the back of the net with an impressive free-kick from distance.
Barca continued to dominate in the remaining stages of the first, although the closest they came getting a second saw Ivan Rakitic forced Jeroen Zoet into a save with a shot from the edge of the box.
Luis Suarez nearly got on the score-sheet after 67 minutes with an audacious effort from distance that crashed against the crossbar with Zoet well beaten.
The home side were not to be denied in the with 16 minutes remaining, as Dembele skipped past two challenges before curling the ball into the far corner.
It was 3-0 a few minutes later as Rakitic's pass over the top found Messi, who buried a strike into the corner from close range.
The Catalan giants were forced to finish the game with ten men after defender Samuel Umtiti was sent off for a second bookable offence.
Messi rounded off the scoring with three minutes remaining with a close range finish to complete his hat-trick.