With the Azerbaijani side on their way out, Richard Almeida thought he had sent Qarabag into the last 32 when his 93rd-minute strike was deflected in off Inter defender Isaac Donkor.
However, the joyous scenes at the Tofiq Bahramov Stadium in Baku were cut short when Leroy George was adjudged offside - giving Dnipro Dnipropetrovsk a lifeline they duly held onto by beating Saint-Etienne in Group F's other game on Thursday.
Inter already guaranteed their place in the knockout stage by winning the group and Qarabag initially looked to be joining them as they were on course to gain a point.
However, Dnipro saw off Saint-Etienne 1-0 to turn up the heat on Qarabag - seeking to become the first Azerbaijani team to progress past the group stage of a UEFA competition.
Instead, Gurban Gurbanov's men slipped to third and will likely look back on what could have been with George appearing to be onside in the midst of a dramatic finale.
The hosts created the first opportunity with a clever double step-over corner routine, but Rashad Sadygov scuffed his shot before Inter's Rene Krhin fired wide at the other end.
It was Qarabag who made much of the early running - Namiq Alaskarov the next to go close with the home side controlling possession in the opening stages.
However, goalkeeper Ibrahim Sehic gave coach Gurbanov a scare when he sliced a clearance high into the air just after the 20-minute mark, although Pablo Daniel Osvaldo could not get the loose ball under control.
M'Baye Niang looked likely to edge Inter in front when he was played clear on goal, but an offside flag thwarted his progress before Qarabag's Vuqar Nadirov was forced off injured.
Juan Pablo Carrizo was required to keep out George's effort from a tight angle in the final throes of the half as Qarabag went in at the break perhaps bemoaning their lack of cutting edge.
Inter began the second period the brighter, with Federico Bonazzoli taking down Osvaldo's cross before seeing his shot deflected wide.
Alaskarov failed to get on the end of Muarem Muarem's teasing delivery from the left as a relatively dour game began to show signs of life.
In a low-key affair, all the drama came at the end as Almeida wheeled away having initially appeared to have made himself the hero with his deflected strike.
The officials were left to field angry complaints from the hosts, however, as Gurbanov's men failed to extend their European campaign into 2015.
