The point is enough to see Atletico return to second position in the table ahead of Real Madrid, while Villarreal, who are now 12 games unbeaten in Spain's top flight, remain fourth.
© Getty Images
It took until the ninth minute for either side to create a half-chance. The opportunity came for Saul Niguez after the Atletico midfielder had shifted the ball from left to right inside the Villarreal box, but his effort was always high and wide.
Indeed, the opening 20 minutes passed without any real incident or even a shot on target. The two top defences in the league cancelled each other out early on, which made it difficult for the players in the final third of the field to make a serious contribution.
It took until the 23rd minute for either team to register a shot on target, but Saul's daisy-cutter was very comfortable for Alphonse Areola in the Villarreal net, before Antonio Rukavina fired harmlessly over the crossbar down the other end.
Saul had the game's only two attempts on target in the opening 45 minutes. His second was a little better than his first, but the midfielder's curling effort was collected by Areola five minutes before the end of a very tight first period in Madrid.
The clearest chance of the first half fell to Antoine Griezmann, but the Atletico attacker, who was withdrawn just past the hour after struggling to impress, could not make proper contract on a cross from Juanfran and his header drifted wide of the post to leave the two teams on level terms at the break.
Atletico came close to making the breakthrough 10 minutes into the second period when Angel Correa's deflected cross headed for the back of the net, but Areola was on hand to make a fine save.
Villarreal had a golden chance to register in the 63rd minute when Cedric Bakambu went through one on one with Oblak, but the Yellow Submarine striker fired wide of the post under little pressure.
Luciano Vietto, who scored 20 times for Villarreal last season, was introduced for Atletico in the 69th minute during a period where both managers looked to their bench.
Leo Baptistao, who is actually on loan at Villarreal from Atletico, was then thrown on 10 minutes from time as the visitors made a positive change in search of a winning goal, but the hosts remained unmoved in defence.
Diego Godin had a half-chance from a corner in the 81st minute, but the Atletico defender headed over the crossbar. Fernando Torres then tested Areola five minutes from time, but once again the save was made.
Perhaps the best chance of the second period came in stoppage time when Vietto drove into the Villarreal box and looked to find the bottom corner, but Eric Bailly, who struggled through the final minutes with cramp, just did enough to prevent the Argentine from winning it against his former club.
It was a frustrating night for Atletico, who have fallen eight points behind the league leaders Barcelona, but they will enter next weekend's clash with Real Madrid above their capital rivals in the table.