Real Madrid remain just one point behind Barca at the top of La Liga and with a game in hand as Karim Benzema scored twice in the absence of Cristiano Ronaldo and Gareth Bale in a 4-1 win at Eibar.
An inspired performance by Messi on Saturday raised Barca hopes of a miraculous Champions League fightback from 4-0 down against Paris Saint-Germain next Wednesday.
And the champions showed no ill effects from Enrique's pending departure in arguably their best performance of the season.
Messi opened the scoring in sensational style on 24 minutes as he turned just inside the Celta half before skipping past a host of helpless defenders and stroking the ball home from the edge of the area.
However, the finish for Barca's second was equally as majestic as Messi's pass was dinked over Sergio Alvarez from close range by Neymar.
The hosts' dominance was rewarded with a third just before the hour mark, although there was more than a touch of fortune about it as Ivan Rakitic was clearly offside when he pounced on Rafinha's layoff.
Messi was the provider once more for the fourth as his low cross was turned home by Samuel Umtiti for his first Barca goal.
And the five-time world player of the year produced another individual effort to end the scoring as it started as he cut in from the right before firing the ball inside Alvarez's near post.
Earlier, Madrid boss Zinedine Zidane praised his side's response to a recent slump in form after defeat to Valencia and a thrilling 3-3 draw with Las Palmas in two of their previous three outings.
"I am happy with our reaction," said Zidane. "In the course of a season there are moments when you have to suffer and it is normal that you can't always play well. "We started very strongly and at a high tempo, which is very important away from home."
Indeed, Madrid were 3-0 up inside half an hour as Benzema finished twice from close range before teeing up James Rodriguez for the third.
"Benzema had a part in all four goals. I am happy for him, he had a great game," added Zidane.
Despite the absence of Ronaldo and Bale through injury and suspension respectively, Zidane rested a host of other first-team regulars ahead of Tuesday's Champions League last 16 return leg away to Napoli.
Those coming in rewarded Zidane's faith in the depth of his squad with the often sidelined Rodriguez a constant threat.
The opener arrived on 14 minutes when Benzema followed up after Yoel had saved his initial effort to register just his second league goal since October.
Madrid soon doubled their advantage when Rodriguez's wicked in-swinging free-kick left Benzema with the simplest of tasks to knock the ball home from point-blank range.
Four minutes later the roles were reversed as this time Benzema's low cross was swept into the far corner on the stretch by Rodriguez for his fifth goal of the season.
Marco Asensio had unselfishly squared to Rodriguez in the move for the fourth goal, but after the Colombian's effort came back off the post, Asensio expertly dispatched the rebound from a narrow angle.
Ruben Pena beat Danilo to Pedro Leon's cross to the far post to fire in a consolation 18 minutes from time.