Valencia's 2-1 defeat at Eibar meant that a victory for Atletico would move Diego Simeone's side directly behind league leaders Barcelona, and Fernando Torres came off the bench to seal all the points for the hosts.
Atletico did not really threaten Alaves until the 14th minute of action - Saul Niguez having a strike deflected just wide of the post after finding space in a forward position.
Atletico were in control of the match as the first period continued to develop, but Alaves were causing problems as El Haddadi was joined by Ibai Gomez from a wide position.
Koke had perhaps Atletico's best chance of the first period in the 36th minute, but the Spaniard's half-volley from a central position was deflected into the arms of Alaves goalkeeper Fernando Pacheco.
El Haddadi then headed a Ibai cross wide of the Atletico post late in the first period as the visitors continued to impress.
The first half-chance of the second period fell to the home side, although Griezmann's effort from the edge of the box failed to test Pacheco between the away side's sticks.
Burgui then had an effort deflected wide of the post down the other end as Alaves looked for the breakthrough goal.
Koke had a decent chance for Atletico just before the hour as the hosts pressed forward, but the midfielder missed the post.
The clash was still goalless approaching the final 25 minutes of football, although the Atletico supporters remained in fine voice as they looked to drive their team to all three points.
Fernando Torres and Yannick Ferreira Carrasco both came off the Atletico bench in the 69th minute, and the former got his name on the scoresheet five minutes later when he converted a low cross from Sime Vrsaljko.
Alaves introduced Bojan late on as they attempted to hit back, but Atletico held on to their one-goal advantage to move within three points of league leaders Barcelona.
Atletico (4-4-2): Oblak; Vrsaljko, Savic, Godin, Luis; Saul (Torres 69'), Thomas (Correa 46'), Gabi, Koke; Griezmann, Gameiro (Carrasco 69')
Alaves (4-2-3-1): Pacheco; Aguirregabiria, Maripan, Alexis, Duarte; Pina (Bojan 77'), Garcia; Alfonso, Burgui, Ibai (Santos 84'); El Haddadi