The victory marked a triumphant start to the Ronald Koeman era, Barca having been engulfed by all manner of turmoil since losing 8-2 to Bayern Munich in its previous competitive match on 15 August (AEST).
An unsuccessful attempt to force a transfer by club talisman Messi was undoubtedly the major headline, but as Barca started its 2020-2021 season, it proved this is not a team to write off lightly.
Fati got the ball rolling with an impressive double in a five-minute period, before then winning the penalty that was scored by Messi, who subsequently saw a cross of his turned in by Villarreal defender Pau Torres.
Unai Emery's side tightened up in the second half, with Barca consequentially having a little less freedom in the final third, but Villarreal's slight improvement had no impact on what was an easy start for Koeman in LaLiga.
With Messi's future up in the air, Fati had seemingly been billed as the poster boy of this new era at Barca and fittingly he was their inspiration here, opening the scoring 15 minutes in with an emphatic first-time finish from Jordi Alba's cut-back.
The teenager was decisive again a few moments later, latching on to Philippe Coutinho's throughball and coolly slotting past the helpless Sergio Asenjo, who also had no answer to Messi's penalty, which was won by the omnipresent Fati as well.
Things got even worse for the visitors on the stroke of half-time, Torres poking Messi's cross beyond Asenjo as the unlikely spectre of Sergio Busquets lurked for a tap-in.
Perhaps unsurprisingly, Barca's intensity did drop after the interval and Villarreal became a more compact unit after a couple of half-time changes.
Koeman took the opportunity to give Fati a bit of a rest with 20 minutes to go, with another talented teenager, Pedri, given the chance to come off the bench for his LaLiga debut after joining from Las Palmas.
Miralem Pjanic and Francisco Trincao were also given their debuts as substitutes, with the young Portuguese winger almost adding a fifth goal when stinging the palms of Asenjo, but Villarreal managed to avoid any further embarrassment.
Barca next ravels to Celta Vigo on Friday (AEST), while Villarreal will hope to bounce back at home to Deportivo Alaves a day earlier.