Luis Suarez had a quiet first home start after his star performance from the bench in last week's 6-1 win over Granada and Atletico only really started to create some danger when he came off and was replaced by Diego Costa.
Costa twice came close to snatching a late winner but failed to connect with dangerous crosses from Yannick Carrasco, while Villarreal could also have found a late goal in an end-to-end finish, as forward Gerard Moreno volleyed narrowly wide.
Villarreal played the better football for most of the game and could have taken the lead in either half through right back Mario Gaspar, who was thwarted on both occasions by excellent saves from goalkeeper Jan Oblak.
Unai Emery's Villarreal provisionally lead the standings with eight points from five games, while Atletico, who started the campaign two weeks later, have taken five from three.
Atletico went into the game looking for a response after being cancelled out by Huesca in Wednesday's goalless draw but again struggled to break down their opponents, and Oblak was critical with his side.
"We were too static in the first half and the more space we found the better we played but we need to play like that from the start. We should have got down the wings more and played more crosses," he said.
"Villarreal planned the game well, they closed us down well in the first half and didn't give us any space. They played well, we could have done more but we didn't do enough to win. We leave here with a draw which we were not looking for."