Having amassed just four points from six league phase matches, Frankfurt were in must-win territory if they wanted to keep their hopes of reaching the knockout stages alive.
However, their task became more difficult within five minutes when they fell behind, as Camilo Duran turned home from close range after Kaua Santos had initially saved Leandro Andrade’s attempt.
Die Adler, though, provided a quick response, with Can Uzun finding the bottom corner from outside the area following some good work from Ritsu Doan down the right flank.
The game was played at a frantic pace for the remainder of the first half, but there were to be no more goals.
The hosts looked more likely to move in front, as Santos needed to be alert to deny Duran before a deflected Andrade attempt almost found the top corner.
Eintracht, meanwhile, forced Mateusz Kochalski into a comfortable stop from distance through Uzun, and Doan missed the target with a first-time effort from inside the area.
Interim boss Schmitt had five days to work with the team before this encounter, but the visitors were unable to put their opponents under any sustained pressure.
Die Adler didn’t manage to work Kochalski until 20 minutes into the second half, and that was only a tame Doan shot. Ellyes Skhiri also had an effort saved, yet Frankfurt lacked creativity.
They were given a helping hand with 78 minutes on the clock when Ansgar Knauff was body checked by Behlul Mustafazade, convincing referee Sandro Scharer to point to the spot. Qarabag were incensed, believing they should have received their own penalty for a similar situation at the other end, yet their protests were waved away before substitute Fares Chaibi converted from the spot.
Nevertheless, they were ahead for fewer than 120 seconds, as Qarabag flew forward and equalised through another Duran tap-in.
Both teams were desperate for a winner in the closing stages, with the reigning Azerbaijani champions also needing a win to consolidate their place in the playoff positions ahead of the final matchday.
And, in the end, it was the Horsemen who struck in the fourth minute of stoppage time through Bahlul Mustafazade, who made up for his earlier mistake by firing into the roof of the net from another low cross to become the first Azerbaijani player to score in the UCL.
The result means Frankfurt have now failed to win any of their past five UCL trips, and they must now turn their attention to the Bundesliga to try and qualify for this competition next term.
Qarabag, meanwhile, have 10 points to their name ahead of the final league phase matchday with a huge chance of finishing in the top 24.
Flashscore Man of the Match: Camilo Duran (Qarabag)