Andrea Stramaccioni's young side may have dominated possession but were left to rue a late goal from the visitors, as Marko Livaja's double appeared to have won the tie
Marko Livaja looked to have been the Nerazzurri's hero on the night with a pair of goals sandwiched in between Rashad Sadygov's rocket from distance early in the second half, but Nicolas Canales headed a famous Azeri equaliser at the death.
Youth was the name of the game once more for coach Andrea Stramaccioni, as the likes of Primavera quartet Vid Belec, Luca Garritano, Andrea Bandini and Simone Pasa were all given rare opportunities to impress in the first team.
However, it was one of their more experienced graduates who staked his claim for a place in the trainer's plans inside 10 minutes, as Alvaro Pereira's cross evaded two Neftchi defenders, allowing Livaja to tap into an empty net.
Inter tried to take advantage of their Brazilian connection in the side, represented by the talents of Jonathan and Philippe Coutinho, but neither player could further their tally before half-time despite promising forays forward.
As ever in football, a failure to take chances paved the way for Neftchi to grab a surprise leveller through Sadygov, who picked the ball up in central midfield and made his way towards goal before rifling home a piledriver from 25 yards out.
But just moments later, on 54 minutes, the Italians looked to the flanks for inspiration and Yuto Nagatomo whipped up a cross for Livaja to head past Sasa Stamenkovic.
Total control of the tie ensued for Inter, but they failed to make their dominance count - Livaja and Coutinho being the guiltiest parties after fluffing good opportunities to extend their slender lead.
And quite incredibly, lightning struck twice as the Azeris displayed superb resolve to stay in the contest. On 89 minutes, Nicolas Canales popped up to head the rebound from Belec's save on Bruno Bertucci's strike.
Despite their valiant efforts in Italy, the Azeri side end their Europa League campaign bottom of the pile in Group H. Inter, meanwhile, will now look forward to the round of 32 in the New Year.