Even without its most creative player at the start, Villarreal picked Osasuna apart thanks to the speed of its forwards.
Jonathan Pereira and Javier Aquino led the way for the visitors in Pamplona.
Moments after driving the ball just across the goalmouth, Pereira beat the offside trap with a perfectly-placed pass to spring Jeremy Perbet behind Osasuna's high defensive line.
The French striker did the rest by resisting the challenge of goalkeeper Andres Fernandez before slotting the ball between his legs.
Pereira played a key part in doubling the lead on the half-hour mark. He collected Bruno Soriano's incisive long pass, dribbled deep into the box, and after momentarily losing control laid off for Aquino to scoop the ball over a defender and into the net.
Coach Marcelino Garcia sent on Dos Santos for Perbet in the 63rd and 12 minutes later he squared Aquino's pass for substitute Ickechuwku Uche to polish off a counterattack.
"When this team is dynamic, when it is well positioned, it's a team that creates a lot scoring chances based on combining well with quick passing," said Garcia. "Playing with speed and precision is what we want to do and what we saw today."
Osasuna lost its best attacking players this offseason and has yet to pick up a point while being outscored 7-1 through three defeats.
Celta dominated Granada at Balaidos Stadium and went ahead in the 29th when midfielder Rafina Alcantara brother of Bayern Munich's Thiago fired in a cross that had taken a deflection to catch goalkeeper Roberto Fernandez out of position.
Celta wasted a slew of chances to double its lead. Alex Lopez hit the post in the 35th before missing again from close range, while striker Charles squandered three excellent looks on goal.
Granada forward Francisco "Piti" Medina volleyed home the 62nd-minute equalizer on the run, arriving from the right side to lash Brayan Angulo's bouncing cross into the net. The visitors did little else in the match.
Lopez curled a long strike off the post again in the 68th, as Celta had to settle for the point and an undefeated record of two draws and a win through three rounds.
"When a team creates so many scoring chances that are the fruit of good play it's a reason to be happy," said Celta's new coach Luis Enrique. "I'm not worried about our lack of scoring touch and I congratulated my team for the match. I am more than satisfied because I continue to think that we are on the right path. To be honest, I didn't expect my team to be playing this well at the start of the season."
After a dull first half at Jose Zorilla Stadium, Valladolid center back Marc Valiente scored after Omar Ramos' corner was flicked on to the center of the area by Carlos Pena in the 47th.
Valladolid was closer to a second goal than Getafe ever was to the leveler, with Omar shining as a playmaker.
Barcelona visits Valencia while Madrid hosts Athletic Bilbao on Sunday, when Real Sociedad welcomes Atletico Madrid, Malaga plays at Sevilla, and Espanyol faces Real Betis.
Levante won 2-1 at Rayo Vallecano and Elche drew 2-2 with Almeria on Friday.
