Thomas Partey's second-half equaliser and the 59th-minute dismissal of Pedro Henrique was not enough to keep the Azerbaijani outfit from holding the LaLiga heavyweights to another stalemate.
Qarabag also defied a numerical disadvantage to register their first ever point in the competition when the teams met two weeks ago, although both sides finished with 10 men here as Stefan Savic received his marching orders for a second yellow in the closing stages.
The visitors looked set to take an easier route to a new slice of history when Spanish midfielder Michel headed them into a 1-0 lead at half-time.
Thomas responded with a spectacular equaliser in the 56th minute and Henrique's sending off for a high boot on Diego Godin appeared to be the help Atletico needed to close the gap on second-placed Chelsea.
Instead, they were yet again frustrated by the underdogs and will need maximum points, and favours elsewhere, to have a chance of progressing to the knockout stages.
Eager to avoid the frustration of their previous meeting, Atletico immediately got on the front foot as Ibrahim Sehic was forced to parry away Antoine Griezmann's well-struck volley from the edge of the area.
The hosts produced an even better move in the 15th minute when Kevin Gameiro was freed by Angel Correa's backheel, only for a heavy touch to allow Sehic to smother.
Gameiro screwed his next shot across the face of goal and a stretching Godin headed over the bar as opportunities continued to go begging.
Jan Oblak was not allowed to relax at the other end, though, with the Slovenian getting down low to his left to deny Pedro Henrique.
But there was little the goalkeeper could do to prevent Qarabag from snatching a shock lead, the Azerbaijani champions rewarded for possession and perseverance as Michel emphatically headed in Wilde-Donald Guerrier's corner.
Gameiro was guilty of wasting another good chance immediately after the restart, the France striker unable to readjust when Sehic pushed Correa's shot into his path.
But just moments after Savic's goal-line clearance rescued them from going two goals behind, Atletico were level.
Griezmann flicked the ball into Thomas' path and, from the right edge of the area, the Ghana international curled a stunning effort into the top-right corner.
And the visitors' hopes of more Champions League history took another blow when Pedro Henrique was shown a straight red for a high boot to Godin's face.
Saul Niguez next saw a header nodded off the line by Rasad Sadiqov, before Filipe Luis shot wide at the end of a classy team move.
Diego Simeone's side repeatedly knocked on the door over the final half hour and came closest to a dramatic winner when a stunning Sehic save denied substitute Nicolas Gaitan and left them four points adrift of Chelsea in Group C.
Their hopes of climbing above either the Blues or Roma were further affected by a late dismissal of defender Savic, who was shown a second yellow for his high challenge on Qara Qarayev.
Key Opta stats:
- Atletico Madrid have drawn three home games in a row for the first time under Diego Simeone (all competitions).
- Thomas Partey has become the first African player to score for Atletico in Champions League.
- Atletico attempted 35 shots against Qarabag, their highest total in a game this season and their highest total in a CL game (since 2003-04).
- Jan Oblak has equaled Zlatko Zahovic as the Slovenian player with the most appearances in the Champions league (32 apiece).