Later on, Lionel Messi saw a strike ruled out by VAR and Ansu Fati wrapped up a fine victory for a rampant Barca two minutes before the end.
"We have played good games before, but today we made the right decisions and finished better," Setien said afterwards.
Griezmann more comfortable in new system
Time will tell whether this match was a one off or is a sign of things to come, but it was a happy return to the starting XI for Antoine Griezmann.
The French forward had started the last two matches on the bench and was sent on only for the dying seconds against former club Atletico Madrid on Tuesday night, but he was back here with a great goal in a positive performance overall.
The 29-year-old curled home a fantastic finish from the edge of the box just before the break and looked much more comfortable in a 4-3-1-2 system with Lionel Messi behind him in a deeper role.
"He played an extremely good game," Setien said. "He linked up really well and he grew in confidence. I'm very satisfied and I'm sure he will be too after such a special goal."
Setien said the goal reminded him of Messi's chip against Real Betis last season and the performance should help to restore calm after the player's family hit out at the coach this week.
Suarez catches Kubala – and gets subbed
Before Griezmann's goal, Luis Suarez scored with a special strike of his own as he beat Sergio Asenjo from a similar spot, curling the ball into the corner with a fabulous finish following a run from Messi.
It was a reminder of what he can do at his best and it brought him level with Laszlo Kubala on 194 goals for the Catalan club. Only two players, Cesar Rodriguez and Messi, have scored more.
Later, he was substituted by Setien for the first time, something the Barca boss had not dared to do before. Perhaps he needed a rest. Or maybe the coach has decided to do things all his own way at last.
Suarez may not reach Cesar on 230 goals and certainly will not catch Messi (630 and counting), but he will surely go on to break 200 and will go down as one of the club's all-time greats – even if it is time for a new and more mobile centre-forward at Camp Nou.
Messi the assistant
Messi went running through Villarreal's midfield to set up Suarez for the first goal and then drew defenders away from Griezmann as he laid the ball off to the Frenchman for the second at the Estadio de la Ceramica.
He later saw a strike ruled out by VAR and a free-kick hit the woodwork, but two more assists took him to 19 in LaLiga, a career-best total, and there are still four more matches to play.
Playing behind Suarez and Griezmann, the Argentine pulled the strings as he so often does and while Villarreal did not defend as well as some of Barca's previous opponents, there were positive signs here.
"Messi, Suarez and Griezmann are players of tremendous quality," Setien said. "We looked for them to be more involved in the middle and it worked out well."
Best performance yet under Setien
This was almost certainly the best Barcelona performance yet under Quique Setien and might have been the team's standout showing on the road this season.
"We tried to find solutions," he said with regard to the team's struggles away from home in 2019-20. "The most important thing was to score. That makes things much easier."
The early goal meant that Villarreal were chasing the game and unlike previous sides such as Sevilla and Atletico, Barca had more spaces to exploit here. But the Yellow Submarine seldom coped with the movement of Barca's front three and Sergi Roberto was effective in a midfield role.
"It's very difficult when they get ahead," Villarreal defender Mario Gaspar admitted. And their coach Javi Calleja said: "It was a deserved defeat. Barca were superior."
...but it's probably too late for LaLiga
Barcelona looked liberated on Sunday and appeared to finally play as Setien has wanted since he took over from Ernesto Valverde in January.
But while that is obviously good news for the Catalans, providing the performance can be replicated from now on, it is likely to be too late in LaLiga.
Setien's side are four points behind Madrid with four rounds remaining and would also lose out if the two teams finished level at the end of the season – because Los Blancos have a better head-to-head record in the two Clasico clashes this term.
"This will help our confidence," the 61-year-old said. "We pressed really well and played a balanced match. But I would like us to have got things right before..."