Barca's captain coolly converted a penalty to put the champions ahead in the 23rd minute.
But anything Olaza could do, Messi could do better, and he did it TWICE with two stunning free-kick strikes either side of half-time.
Messi scored another goal apart from scoring the two free-kicks and consequently equalled his rival Cristiano Ronaldo's record for most hat-tricks in La Liga.
"We have a very big advantage, we have the best player in the world on our side who is also the best at taking free kicks", said Busquets in praise of Messi.
"It was really difficult for us in the first half, with their high press that made it hard for us to play out and we didn't have much rhythm in our play".
There was a subdued atmosphere at the Camp Nou on Saturday and close to 30,000 seats were left empty.
The defeat was Celta's fifth in a row and newly appointed head coach Oscar Garcia will have his work cut out as he tries to lift them out of the bottom three.
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.
"It's a skill he's mastered to perfection", Ernesto Valverde said about Messi's freekick abilities.
"He dominates the art of free-kick taking, and opponents know they can not afford to give away fouls near our area".
"We had a damaging defeat the other day and we needed a win tonight".
Barcelona later confirmed right-back Nelson Semedo would be out for around five weeks with the calf problem which forced him off after 23 minutes.