Ferran Corominas (45+1') opened the scoring for the Gaurs late in the first half. Robbie Keane (50') replied with an equaliser soon after the break. Strikes from Hugo Boumous (70') and Brandon Fernandes (77') ensured the Goans cruised to a quarter-final tie against Jamshedpur FC.
Keane paired up with Robin Singh in attack and Sibongakonke Mbatha and Zequinha were on the flanks. With Conor Thomas in midfield and Jordi Figueras in defence, ATK made use of the maximum allowance of five foreigners in the lineup.
On the other hand, without their head coach Sergio Lobera, his assistant Derrick Pereira missed the services of Ahmed Jahouh and Manuel Lanzarote. However, ISL golden boot winner Coro led the attack with Boumous supporting him.
Goa's Edu Bedia dictated proceedings from the centre of the park, displaying his full array of passing techniques. The Spaniard created a host of opportunities but the strikers failed to get going early on, as he himself missed one.
ATK had their first sniff at the other end when Robbie Keane pounced on a loose ball inside the box and it kissed the crosspiece, taking a deflection off Chechi.
Bedia came clean in the added time of the first half. He split the ATK defence, playing a pin-point forward pass for Coro. Ashutosh Mehta failed to track back, giving his guard away and the Spaniard made no mistake to break the deadlock at the stroke of the whistle.
Rejuvenated after the setback, ATK got their equaliser five minutes after the change of ends. Zequinha's header into the box was flicked towards the far post by Anwar Ali and Keane, oozing with poise and gravitas slotted home.
Moroccan national Hugo Boumous appeared to be in a hurry to win back the lead and so he did after three unsuccessful attempts past the hour mark. Narayan Das played into Coro in the centre who flicked a lob over the ATK defence for Boumous.
The former Ligue 2 player seemed to be offside but with Anwar Ali failing to intercept, the 22-year-old continued his run into the box and slotted past Poirei.
Robin Singh had a few swipes at the other end but the India international's season was perfectly summed up on the night with the rub of the green not going his way.
With a quarter of an hour to go, Brandon Fernandes' shot was saved by Poirei. The winger did get his revenge a couple of minutes later. It was again Das from the left and Coro's flick inside the box that saw the former Churchill Brothers man finish off in style.
ATK's disappointing season came to an end. Earlier, the two-time ISL champions had finished only a place above the bottom in the league. Player-manager Robbie Keane tasted defeat for the first time in his third game which potentially could be his last as a player, given he will be 38 next season.
For FC Goa, it will be a clash with another ISL team for a place in the semi-finals on 12 April, at the same venue as they take on Jamshedpur FC.