Ansu, 17, scored twice inside the opening 20 minutes in Barca's first official outing since they were beaten 8-2 by Bayern Munich in the Champions League last month.
All the headlines were written by Ansu. If last season was his breakthrough campaign, this could be the year he establishes himself in the Barca team. He took both his goals well and his pace is something the side have been lacking since Neymar was sold in 2017.
As well as Ansu, there was also a glimpse of the future in debuts for Pedri, 17, and Francisco Trincao, 20, who both came off the bench. It looks like Koeman will give them plenty of minutes this season.
Only time will tell if Barca have turned the page from last term's trophyless season. They appeared to work harder and press more under Koeman, but tougher tests await them.
Despite easing to three points, Barca still looked susceptible to conceding at the back. No new defenders have arrived yet and there's no real backup to an ageing Gerard Pique and Clement Lenglet. At least Sergi Roberto will have some competition soon. American right-back Sergino Dest will sign from Ajax in the coming days.
Manager rating out of 10
8 -- A dream debut for Koeman on the bench. He couldn't have wished for a better, or faster, start to the La Liga season. It looks like he will stick with a 4-2-3-1 shape this season and his selection of Ansu proved a masterstroke. The Spain international wasn't a regular under Quique Setien.
DF Sergi Roberto, 5 -- Struggled to get involved in attack and at one time appeared to confuse himself on the ball. His position is under threat when Dest arrives.
DF Gerard Pique, 6 -- Despite offering to leave after the Bayern loss, Barca were never going to get rid of him. His experience helps a lot at the back but his minutes need to be managed better moving forward.
DF Clement Lenglet, 7 -- The Frenchman's passing game is constantly evolving and he produced another assured display against Villarreal.
DF Jordi Alba, 7 -- Ran up and down the flank, setting up the first goal for Ansu and linking well with Messi. Came close to scoring himself, too, only to be denied by Sergio Asenjo, who kept the score down on the night.
MF Frenkie de Jong, 6 -- Already looks more confident in a more familiar role under Koeman. A solid start to the season and the expectation is he will only get better.
FW Antoine Griezmann, 6 -- There were complaints that he wasn't involved enough but his tireless running created the space for both of Ansu's goals. His moments of glory will come.
FW Philippe Coutino, 7 -- Set up Ansu's second goal and only an outstanding save from Asenjo denied him one of his own. Looks desperate to take his second chance at Camp Nou after returning from his loan at Bayern Munich.
FW Ansu Fati, 9 -- There can be no doubts now that he is a star in the making. Took his goals like someone twice his age and is increasingly mature in his decision-making.
FW Lionel Messi, 7 -- Played with a smile on his face despite pushing for a summer exit. Scored a penalty and delivered the cross which Torres headed into his own net. Only Asenjo stopped him from scoring more.
FW Ousmane Dembele, N/R -- Came through the game unscathed and Barca will hope this can be the season he finally remains injury-free.
FW Pedri, N/R -- The attacking midfielder, who's a month younger than Ansu, came on for his debut after signing from second division Las Palmas.
FW Francisco Trincao, N/R -- Looks a real talent. Was only on for a short time but came close to scoring.
MF Miralem Pjanic, MF -- Even on this brief display, looks likely to be De Jong's midfield partner this season.