The one that got away. Years later, Tipperary's legendary midfielder Theo English would admit: "We were the luckiest team ever to win that All-Ireland," of the 1961 decider between Tipp and Dublin.
"We won against the run of play, a medal I always say we should never have won."
Fifty-seven years on and Jimmy Gray, Dublin's legendary goalkeeper of that day, agrees.
It's impossible to know the affect a win would have had on hurling in the capital in the subsequent years but Gray is in no doubt.
"We should have won that All-Ireland," he says now. "I think it was only in the second-half that we realised that we could have won it."
As it went, Dublin sensed some vulnerability in a Tipperary team carrying injuries.
Des Foley gave English what the great Tipp man admitted himself was "a fair roasting".
Achille Boothman, who Gray describes as one of the finest hurlers, kept John Doyle under tight wrap. But late on, Tipp got a point that by most people's judgement, should never have been to level the match.
"A lot of people I knew were stewarding at the Nally Stand and they all agreed it was well wide," Gray remembers.
"I would always hold the view that it was about a yard wide."
Tony Wall, Tipperary's star centre-back of that era, was forced off injured but it would turn out to be to Tipperary's benefit.
"They had a guy called Willie Jackson," English would later recall, "he got two balls inside our backline and all he had to do was keep going and pick his spot but he parted too early with the ball, about 20 yards out, and Donal O'Brien stopped them.
"Jackson had the match in his hands but that bit of inexperience caught him.
"When Wall went off, Devaney went centre-back, and played a blinder, cleared a lot of ball. He won the match for us."
Dublin lost by a point, 0-16 to 1-12, and the county has never been as close to capturing the Liam MacCarthy since.
"We were very disappointed about it," admits Gray now.
"Because that was a good team. We were there for a few years.
"Kilkenny beat us in a Leinster final in '59 with a goal in the sixth minute of injury time. And afterwards we beat Kilkenny and Waterford, who played in the All-Ireland final, when we played them in the League."
Like a morgue
Another of Dublin's team, Larry Shannon, recalled later how "The dressing-room afterwards was like a morgue. That's the one thing I'll always recall. The reception took place in a hotel in Lucan that night.
"We were all so down. The atmosphere was like a wake. Nobody was in any form for it after losing the All-Ireland final by a point."
That era was a hugely significant one for Dublin hurling, not merely for their rise to competitiveness but for the constitution of the team.
"For Dublin to have won that All-Ireland in '61, considering it had been 1938 since their previous success, would have been a major achievement, especially so given that it was practically an all-Dublin team," as Gray explained.
"A decision was taken some time in the mid-50s, that the players who came through the minors ranks would be the ones that were picked on the Dublin teams.
"It continued right up until the 70s, when it was relaxed a bit. From '57 to '64, Dublin were up there with the best of them with virtually a Dublin-born team. Paddy Croke was the only non-native on the team.
"We were in two Leinster finals afterwards against Kilkenny and were beaten. But it was a very good team and we should have achieved more."
There was an attendance of 67,000 at the 1961 All-Ireland SHC final but Gray doesn't recall any sort of hurling hysteria breaking out in Dublin at the time.
"I wouldn't have thought there was a buzz," he says. "It hadn't really caught on at the time.
"Football and soccer were very prominent at the time.
"So we wouldn't have drawn huge crowds at the time."
If they didn't capture the public imagination in 1961, nothing that came directly after it was likely to drag the city with them.
Mostly, that was it for Dublin hurling until the stirrings in the county at the turn of the millennium, prompted by the establishment of the development squads and the implementation of new coaching structures in big clubs.
Gray, meanwhile, went on to act as chairman of the Dublin County Board for over a decade and was instrumental in the appointment of Kevin Heffernan to the job of senior football manager in 1973, the moment that would change Dublin GAA forever.
He also chaired the Leinster Council for a spell and managed the Dublin hurlers between 1993 and 1996, succeeding Lar Foley in the role, although the capital had entered a lean period for hurling that take would some time to emerge from.
Indeed, the next time he got his hands on silverware, he was handing the Delaney Cup to Johnny McCaffrey in 2013.
In 2013, Anthony Daly's team bridged the gap to Gray's '61 side by beating Galway in Croke Park and winning the Leinster SHC title for the first time in 52 years.
And on the day, Gray was plucked from the crowd and pressed into service.
"I have to say I was very flattered to be given the opportunity," he says now.
"It was (then Leinster Council chief executive) Michael Delaney who engineered that.
"I didn't know anything about it. I was getting up to go out after the match and he just grabbed me and brought me away.
"It was only when I got to the podium that I realised what I had to do.
"I was very flattered to be able to do it," adds Jim, whose son Tom is the current Dublin minor football manager.
If that was a peak for Dublin, they currently graze somewhere on the mid-slopes of the game's elite.
Tipperary in Thurles was about as tough a draw as they could get for this round of qualifiers and though Gray isn't expecting a miracle in Thurles tomorrow, he is confident of another spike in fortunes for hurling in the capital.
"I don't think people are giving Dublin the credit they're due," he insists.
"They're a very young side. And they're marvellous hurlers.
"They just have to get a bit cuter in the ways of hurling at that level. But that will come."
"They're a fine side and given another year or two, they'll come good."