Alaves failed to make the most of their chances as Atletico Madrid left Mendizorroza frustrated with a goalless draw.
The hosts should have taken the lead on the half-hour, but Brazilian forward Deyverson somehow headed over from point-blank range after Victor Laguardia had hooked the ball onto the crossbar.
Atletico could have scored a late goal when Nicolas Gaitan raced clean through, but goalkeeper Fernando Pacheco dived in to take the ball off his feet.
At the other end, defender Theo Hernandez, on loan at Alaves from Atletico, then forced a fine save from Miguel Moya before tempers boiled over following the final whistle.
Atletico Madrid captain Diego Godin and Deyverson appeared to spit at each other when players from both sides squared up.
Diego Simeone's Atletico are in fourth but lost the chance to close up on the leaders, and will now regroup for next week's Copa del Rey semifinal against Barcelona, when Alaves will tackle Celta Vigo.
Celta Vigo continued their momentum from knocking Real Madrid out of the Copa del Rey in midweek by securing a 2-0 victory away at Leganes.
Alvaro Lemos fired the visitors into a 32nd-minute lead with a neat turn and low shot into the bottom corner.
A penalty from John Guidetti in the 66th minute secured the points for Eduardo Berizzo's side, who move up to seventh.
Saturday's early kick-off saw Villarreal win for the first time in six matches as they beat Granada 2-0 at El Madrigal.
Bruno Soriano scored in the first half and Alvaro Gonzalez in the second as Villarreall remained sixth and in position to fight for a spot in the European competitions next season. Granada are last after their fourth defeat in the past five matches.
Forward Alexandre Pato was not in Villarreal's lineup while he negotiates a move to Chinese club Tianjin Quanjian.
Eibar saw off Deportivo La Coruna 3-1 in a victory at home, thanks to two early goals from Adrian Gonzalez and Sergi Enrich
Emre Colak struck back quickly for Depor, but the visitors could not find an equaliser and Florian Lejeune scored in the second half to seal the three points for Eibar.