In the first ever meeting between the two sides, Duffy's late header rescued a point for the home side after Emin Makhmudov's incredible strike on the stroke of half-time had put the away side into a shock lead.
In the opening ten minutes, Ireland could have been at least two goals ahead through Aaron Connolly and Matt Doherty after a pulsating start in front of 21,287 supporters. Doherty went close with a header on five minutes, after a beautiful ball from Cullen and just 60 seconds later, Idah did brilliantly to run down the end line to square to Connolly, whose shot was blocked.
Captain Coleman’s effort went just wide on ten minutes too, as the Irish supporters urged their side to find the opener. Ireland continued to create and had two good chances halfway through the first-half.
Molumby’s effort from the edge of the box went close, before Connolly's brilliant cross found Idah who headed just wide of the right-hand post. However, in the final moments of the first-half, Emin Makhmudov found himself 30 yards from goal, and under no pressure, he found the perfect strike into the top right-hand corner.
Ireland enjoyed prolonged spells of possession in the second 45 but were left frustrated time and time again as Azerbaijan sat back with every player behind the ball. Parrott’s effort from the edge of the area was well saved before Idah’s glancing header went just wide.
Robinson and Hourihane were introduced and the introductions helped Ireland's cause. Duffy went close, heading just over from Robinson’s brilliant cross as Ireland adopted a more direct approach in the final quarter of the game.
Robinson was agonisingly to finding an equaliser with 10 minutes left but sent his effort wide from the six-yard box, but soon after, that equaliser finally came. Cullen’s deep cross found Duffy, who had stayed up from a corner, who headed home much to the delight of the Green Army behind the goal, for a long-awaited equaliser.
Five minutes of added time were announced, and Ireland piled forward looking for the winner. Robinson went close again but his effort was well saved, and it proved to be the last action of the evening, as Ireland secure their first point of the campaign
Republic of Ireland: Gavin Bazunu; Matt Doherty (James Collins 79), Seamus Coleman (C), Shane Duffy, John Egan, James McClean; Jayson Molumby (Conor Hourihane 62), Josh Cullen (Alan Browne87); Troy Parrott (Callum Robinson 62), Adam Idah, Aaron Connolly (Daryl Horgan 46).
Subs not used: Caoimhin Kelleher, James Talbot, Ryan Manning, Andrew Omobamidele, Jeff Hendrick, Jamie McGrath, Ronan Curtis.
Booked: Jayson Molumby (56), Alan Browne (90)
Azerbaijan: Shakhrudin Mahammadaliyev; Gara Garayev, Maksim Medvedev © (Abbas Huseynov 70), Hojjat Haghverdi, Elvin Badalov, Anton Krivotsyuk, Emin Makhmudov, Tural Bayramov, Namik Alaskarov (Rustam Akhmedzade 70), Mahir Emreli (Ramil Sheydayev 79), Filip Ozobic (Anatolii Nuriyev 80).
Subs not used: Aydin Bayramov, Mekhti Dzhenetov; Rahim Sadikhov, Azer Salahli, Vugar Mustafayev, Ismayil Ibrahhimli, Bahlul Mustafazade, Tamkin Khalilzade.
Booked: Anton Krivotsyuk (67)
Referee: Jerome Brisard (France)
Attendance: 21,287
Carlsberg Man of the Match: Adam Idah