The Argentine superstar bagged two free-kicks and penalty to claim his 34th hat-trick in the Spanish top fight, equalling the record of Ronaldo's 34 hat-tricks.
Sergio Busquets added another in the 85th minute to complete the comprehensive win on the night.
The Argentina international's return from injury has coincided with Barça's sudden resurgence, and Ernesto Valverde's side sit top of La Liga after 12 games, level on points with fierce rivals Real Madrid.More news: Dimitar Berbatov states his prediction for Man United v Brighton
Four minutes later he sent Barcelona back ahead, with a perfectly placed free-kick of his own, which arced beyond the helpless Ruben Blanco in first-half stoppage time.
Valverde said: "It's impossible not to depend on Messi".
"Messi, apart from scoring goals, has a commitment to the game".
Celta Vigo, playing their first game under new manager Óscar Garcia, started brightly as they looked to test a Barcelona side condemned to a shock 3-1 defeat by Levante last weekend.More news: Podcast hosts delete TI 'hymen' episode, apologize for laughing
"With Leo in the team, anything is possible", Valverde was quoted as saying by Marca.
The former Brighton and Watford manager, who started his career at the Nou Camp, said: "We wanted to go out, be courageous and win".
After a disappointing result in the UEFA Champions League earlier this week, Messi took it upon himself to get Barcelona back on the winning trail as they defeated Celta Vigo at the Camp Nou. He has a very high percentage of fouls, you cannot avoid making mistakes in that area.More news: Grace Millane murder trial: Jury hears evidence of clean-up
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