Messi was again Barca's savior and his contribution helped produce a score which flatters a side that struggled especially in the first half to produce the fluid football that has characterized their game over recent seasons.
New Celta coach Oscar Garcia, a former Camp Nou veteran, set his side up to push Barca high up the field and Barca were under pressure until Messi opened the scoring from the penalty spot after Joseph Aidoo handled Junior Firpo's ball into the area.
Celta equalized from an excellent free kick three minutes before halftime with Lucas Olaza beating Ter Stegen after a foul committed by Messi.
The Argentinean made amends in first half injury time by scoring a majestic free kick of his own from 25 yards and he repeated the feat three minutes into the second half to complete his hat-trick.
Antoine Griezmann, who struggled again to make an impact, saw a shot well saved by Celta keeper Ruben Blanco as Barca, now with Sergio Busquets on the pitch following Nelson Semedo's injury midway through the first half, giving Ernesto Valverde's side much more control of the ball.
The midfielder got his reward with a rare goal six minutes from time when he had time to control a loose ball at the edge of the Celta area before beating Blanco with a powerful shot.
Real Madrid produced an assured display to win 4-0 away to Eibar in a rain-swept Ipurua Stadium.
Zinedine Zidane's side was 2-0 up after 20 minutes thanks to a Karim Benzema goal, which makes him the 6th highest scorer in Madrid's history, and a Sergio Ramos penalty after a foul on Eden Hazard.
A second penalty, this time scored by Benzema just before the half hour, made it 3-0 and with the result already decided, Fede Valverde's first league goal for Madrid closed the scoring with just under half an hour left to play.
Valencia continued their positive run of form with two goals in the second half minutes to give them a 2-0 win at home to Granada, who have now lost their last three games.
Daniel Wass opened the scoring in the 74th minute after taking advantage of being pushed into midfield from right back and youngster Ferran Torres sealed the win deep in injury time with a left-foot shot from outside of the penalty area.
Saturday kicked off with Alaves maintaining their impressive home record with a 3-0 win at home to Valladolid.
First half goals from Joselu on 28 minutes and a second four minutes later from Tomas Pina following a howling error from Valladolid keeper Jordi Masip put Alaves on their way before Lucas Perez rounded off the scoring from the penalty spot in the second half with a goal that means he has now scored in each of Alaves' last seven games.
Friday saw Javier Aguirre begin his reign at bottom of the table Leganes with a hard-fought draw away to high-flying Real Sociedad in a rain-swept Anoeta Stadium.