The hosts drew a blank at the Calderon and failed to keep pace with leaders Barcelona, who now enjoy an eight-point advantage at the top of the Primera Division
Following a hard-fought 2-1 win at struggling Las Palmas on Saturday, defending champions Barcelona were able to enjoy Real Madrid being held 1-1 at Malaga before Atleti were also held to a share of the points.
Antoine Griezmann wasted the hosts' clearest opening and was substituted during a feisty encounter at the Vicente Calderon that leaves Diego Simeone's team eight points behind Barcelona with 13 matches remaining this season.
Villarreal striker Cedric Bakambu might have sent Atleti into next weekend's Madrid derby level on points with Real but botched a glorious opportunity after the hour.
Nevertheless, the fourth-placed visitors were able to extend their impressive unbeaten run in La Liga to 12 matches.
Marcelino rested Denis Suarez, Mateo Musacchio, Manu Trigueros and Leo Baptistao among his substitutes, with an eye on Villarreal's Europa League trip to Napoli on Thursday, but his side began confidently.
Samu Castillejo had an early penalty claim turned down when he was clumsily challenged by Atletico midfielder Saul Niguez.
As expected, in a showdown between the two most miserly defences in La Liga, chances were at a premium.
Speculative efforts at either end from Saul and Castillejo offered fleeting encouragement that the match might break free from its pattern of cagey intensity, before Villarreal defender Daniele Bonera lashed a 32nd-minute corner over when he should have worked Jan Oblak in the Atleti goal.
The hosts' best chance of the opening period came five minutes before half-time but Antoine Griezmann did not get enough on his header from Juanfran's superb cross.
Atletico pinned Villarreal back after the restart, with goalkeeper Alphonse Areola acrobatically tipping Angel Correa's chip over the bar.
Nevertheless, a dissatisfied Simeone hauled off star forward Griezmann in the 62nd minute and almost watched his men go behind moments later.
Bakambu had been largely starved of service but could have made himself the match-winner when he latched onto a throughball from Antonio Rukavina, only to blaze wildly over.
Mario Gaspar made a vital block at the other end when Areola failed to claim a corner and Saul shot goalwards.
Former Villarreal forward Luciano Vietto scored the winner in last season's corresponding fixture and almost did likewise for Atletico, coming off the bench to fire into the side-netting under pressure from Eric Bailly in stoppage time.
His former employers held out for a deserved share of the spoils and they retain an eight-point advantage over fifth-place Sevilla in their quest for La Liga's final Champions League qualification berth.