Captain for the day Raul Garcia headed in the only goal of the game after 14 minutes, but the hosts created few further opportunities and spent the latter stages holding on amid Villarreal pressure.
And they survived a scare in the final minute when Toby Alderweireld diverted a cross just inches wide of a post.
This hard fought triumph was Atletico's third consecutive 1-0 win at home in the league, highlighting both Simeone's team's resilience and his thin resources.
With top scorer Diego Costa and Arda Turan injured and captain Gabi suspended, Simeone had to pull together a makeshift side, giving starts to Cristian Rodriguez, Diego and Mario Suarez, while Alderweireld deputised for Miranda in defence.
Atletico were unable to trouble Villarreal's backline after the break, their only attempts a soft effort by David Villa easily caught by Sergio Asenjo, a low shot from Garcia that the goalkeeper also gathered comfortably and a scuffed drive from substitute Tiago Mendes that went well wide.
And home hearts were in their mouths when Alderweireld's attempted clearance went across the face of the goal, but the Calderon breathed a huge sigh of relief as it dropped wide, leaving Simeone's side still in charge in the title race.
Barcelona produced an unconvincing display against Real Betis but still beat the Primera Division bottom side 3-1 to keep the pressure on Atletico.
Lionel Messi opened the scoring from the penalty spot after 15 minutes and Jordi Figueras, who had conceded the spot-kick, doubled Barca's lead with an own goal midway through the second half.
Betis striker Ruben Castro quickly pulled one back for the visitors but Messi struck again in the 85th minute, reacting quickly to having a penalty saved to send the ball in on the rebound and seal the three points.
Before kick off, fans showed their opposition to the FIFA-imposed transfer ban on Barcelona - a punishment for signing under-age overseas players to the club's famed academy La Masia - by unfurling a huge, eye-catching banner with the message "La Masia shall not be touched".
Gareth Bale took advantage of a goalkeeping howler to help Real Madrid claim a deceptively-difficult 4-0 victory at Real Sociedad and keep the pressure up on Atletico and Barca.
With the top two having already won on Saturday, Madrid knew anything other than victory at the Anoeta could spell the end of their title challenge, but they came away with the three points thanks to goals from Asier Illarramendi, Bale, Pepe and Alvaro Morata.
Former Sociedad player Illarramendi opened the scoring against the run of play on the stroke of half-time and then Bale - despite suffering a gash to the knee moments before - doubled the lead in the 66th minute, thanks largely to a huge error from home goalkeeper Claudio Bravo.
Bravo's attempt to kick the ball out of hand to a team-mate near the touchline ended up going straight to Bale 35 yards out, and the Wales international took a touch before slamming his shot into the unguarded net as Bravo scrambled to get across.
That goal was followed by two more late strikes from Pepe and Morata as Madrid claimed an impressive victory that keeps them within three points of leaders Atletico and within two of Barca.
Rayo Vallecano cruised to a key 3-0 win over Celta Vigo to ease their relegation worries.
Rayo began the weekend just three points above the drop zone but end it firmly in mid-table and above Celta on their head-to-head record.
Ruben Rochina scored the opener in the 26th minute and a quick double from Alberto Bueno in the second half ensured Rayo were not even rocked by Razvan Rat's 64th minute red card.