Qarabag earned their first ever Champions League point when they played Atletico in Azerbaijan two weeks ago, a match in which they also finished with 10 men.
Atletico again had a difficult time creating significant scoring chances against Qarabag, who played solidly defensively and took advantage of one of their few opportunities to break the deadlock.
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Midfielder Michel scored with a header after a corner kick in the 40th minute at the Wanda Metropolitano Stadium.
Atletico equalised in the 56th minute with a stunning side-foot shot from outside the area by midfielder Thomas Partey, hitting the top corner after a back-heel set up by forward Antoine Griezmann.