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Following the win, Alaves temporarily holds the third spot in La Liga with 23 points, on goal differential behind Atletico Madrid, while Huesca remains dead last in 20th with six points.
Godin pulled a muscle in the 64th minute on Saturday as Inaki Williams gave Bilbao a 2-1 lead at the Wanda Metropolitano, but Atletico's captain stayed on.
Dortmund handed Atletico their heaviest defeat under Diego Simeone with a 4-0 victory 13 days ago but this contest was almost a mirror image, the hosts in control from start to finish.
Griezmann's bending effort in the second half looked likely to prove the difference in a contest short on chances at Butarque but Guido Carrillo's 82nd-minute equaliser earned Leganes a deserved point
Diego Simeone declined to comment on the situation of Gelson Martins, who has made only three appearances with the Rojiblancos since joining the club over the summer.
Atletico Madrid lead second-placed Barcelona by one point, with Real four further adrift, with the two giants to face off at the Camp Nou on Sunday.
Dortmund were without in-form Spanish striker Paco Alcacer, while Diego Costa returned to partner Antoine Griezmann up front for Atletico.
Champions League: Facing Atletico Madrid is like toothache for Borussia Dortmund goal-ace Paco Alcacer
The 25-year-old, on loan from Barcelona, has needed just 106 minutes to score seven Bundesliga goals this season -- the best goal-rate in the league's history.
Madrid had already lost 3-0 at Sevilla, drawn 0-0 with Atletico Madrid, and lost 1-0 at CSKA Moscow before a humiliating 1-0 defeat at Alaves on Saturday.
Barca started the day at the top of the pile and then Atletico Madrid enjoyed a couple of hours at the summit after edging past Real Betis at the Wanda Metropolitano.