Real Sociedad moved up to fifth place in La Liga with a 1-0 win over Granada, while Osasuna and Sevilla played out a goalless draw.
Sociedad's win catapulted them five places up the table from 10th to fifth place for their second win of the new campaign.
Osasuna managed to rebuild their battered pride after they were annihilated 8-0 by Barcelona on Saturday with a plucky performance.
Daniel Estrada's second-half goal earned Philippe Montanier's side victory against one of the division's newly-promoted sides.
Estrada's strike came in the 64th minute when he linked up with Asier Illarramendi to curl his shot into the top left-hand corner of the goal from 25 yards.
Both sides took time to settle down, with the first real chance of the game coming from Sociedad's McDonald Mariga in the 12th minute, but his speculative 25-yard strike flew over the bar.
The best chance of the first period came when Illarramendi delivered a testing corner, which Inigo Martinez headed from inside the six-yard box, causing Roberto to tip the ball over the bar.
Granada midfielder Daniel Benitez then saw his 20-yard volley caught by goalkeeper Claudio Bravo on the stroke of half-time to leave the scores locked at 0-0.
After the break, the home side had more of the attack, with Carlos Vela's shot missing the target just minutes before Estrada broke the deadlock.
Osasuna will look back on their game with a tinge of regret as the Sevilla goalkeeper Javi Varas produced a string of top saves.
Manuel Lolo tried his luck twice in the early stages, with a 30-yard strike held by Varas who then superbly tipped Lolo's next effort around the post.
Sevilla's first effort was a wildly ambitious long-range effort wide from Jesus Navas, before Lolo curled a free-kick wide at the other end after Federico Fazio's foul on Lamah.
Osasuna keeper Andres Fernandez's first test came when Martin Caceres headed Manu Del Moral's corner goalwards, and Fazio then nodded a Navas delivery wide.
Emiliano Armenteros volleyed over for Sevilla as half-time arrived with no score, but Varas was again quickly into the action as the second half started, saving Francisco Punal's drive.
The best chance of the half fell to Francisco Nino who headed over and then saw another effort tipped behind by the impressive Varas but both teams failed to score.
Rossi on target
Villarreal claimed first win of the new Primera Liga season at home to Real Mallorca.
Giuseppe Rossi and Nilmar scored early in each half although the hosts could have scored even more as they enjoyed a return to form at El Madrigal.
On another night Rossi could have had a hat-trick but it mattered little as the Yellow Submarine ended a winless start to the season that had seen them second from bottom before tonight.
Rossi had already forced a save from Mallorca goalkeeper Dudu Aouate before he grabbed the opener on eight minutes.
The Italy international had his first effort blocked by Mallorca goalkeeper Dudu Aouate but from a similar distance he made no mistake with a low left-footed shot.
Six minutes after the re-start Villarreal got themselves the breathing space of a 2-0 lead.
Nilmar ran onto a Borja Valero pass and sent an angled shot into the bottom-right corner.
From there it was always going to be a tough task for a Mallorca side whose only goal this season came through De Guzman on the opening day before his move.