Terry Venables was their manager in those days and apart from Gascoigne they also had Gary Lineker, but change was in the air even before Des Walker's own-goal took the Cup back to White Hart Lane.
The arrival that summer of Alan Sugar as club chairman was the start of the rocky road that led to Graham's appointment after eight turbulent and trophy-less years. Other managers came and went, many high-profile players too and, unlikely as it may seem, only Justin Edinburgh, their much-maligned left-back, has survived it all - and he has his Cup winners' medal to help him tell the tale to anyone who cares to listen.
"The others are all bored of me talking about it by now," Edinburgh admitted this week at Spurs Lodge, the training ground deep in the heart of Birds of a Feather country where Tottenham have been preparing for what they hope will be a triumphant return to Wembley. "I keep letting them all know about it - they don't want to see the medal but I do let them know about it whenever the subject comes up."
Edinburgh has never strayed far from his Essex roots, joining Southend United before moving on to Spurs at the age of 20. The Cup final came at the end of his first full season there. "I'm just hoping I'll be able to take a bit more in this time," he said. "In 1991 I'd just come from the Fourth Division and things happened too quickly for me to appreciate what it was all about. I just remember thinking afterwards that it was going to happen to me every year."
If only he'd known. A new manager every year was more like it. After Venables it was Peter Shreeves, then Ray Clemence and Doug Livermore, Ossie Ardiles, Gerry Francis, and then came Christian Gross. When it comes to the subject of Graham's immediate predecessor, Edinburgh does not hide his feelings. "I was not involved - again - on a Saturday and I was at a friend's wedding, driving from the church to the reception. I heard the good news on the radio that my "friend" Christian Gross had been sacked. I was celebrating two things that day, that's for sure."
Having been told by Gross he was surplus to requirements, Edinburgh seemed on his way out of the club a few months ago but, like many of his team- mates, Edinburgh has found a new lease of life under Graham. "It's still a transitional period but the club's finding some stability with George and the speed of it has been remarkable," he said. "This is the best it's been since I first arrived. He's cut out a lot of the sloppiness and the lateness, training is more high-tempo and he's instilled a lot more self- belief in the players.
"At the start of this season I didn't think we were going to do any better than we did last season because we lacked confidence, the players were becoming despondent and we didn't really feel we had a leader. And if you haven't got any belief in the person in charge of you things aren't going to go too well. But George is definitely a leader and he's showed us the way to go."
Life has improved for Edinburgh to such an extent that he not only finds himself playing regular first-team football once more, he was even accorded the privilege of being "rested" for Tuesday's FA Cup tie with Barnsley. "I didn't think I'd ever see the day," he said. "Perhaps David Ginola or Darren Anderton. But it's a nice compliment."
In reality, though, the arrival of Mauricio Taricco from Ipswich Town, one of Graham's first signings, has increased the pressure on Edinburgh, although with Taricco Cup-tied Edinburgh is sure to be playing Ginola's straight man on Tottenham's left flank again tomorrow. "It can be frustrating at times," he said, "but it's very easy for me when I get the ball because it doesn't matter how many players David's got around him, he always wants the ball.
"Going the other way can be more difficult because you might have two players running at you, but you accept that because you know what David can do with the ball at the other end. Playing behind him can be difficult, but more often it's enjoyable because it's nice to watch him tormenting other defenders - he does it to me often enough in training." For Edinburgh, and for Tottenham, it has been quite a wait, but you get the impression their longest-serving player is relishing every moment.