AMID the haze of time and booze that has obscured their recollections, the one thing they all remember is the clock.

Even 30 years on, Paul Hegarty swears it stopped at 4.30pm, while derby veteran Hamish McAlpine confesses it was only that afternoon that he first noticed it hanging above the tunnel at Dens Park. It is no longer there, having apparently been removed on safety grounds, but it retains a special place in the memories of the players who earned Dundee United their solitary Premier League title.

It was on this day in 1983 that Jim McLean's side won the league at Dens, beating their city rivals 2-1 to hold off the challenge of Celtic and Aberdeen, who had celebrated a trophy of their own in Gothenburg just three days earlier and would go on to secure the Scottish Cup the following weekend. It made for a remarkable climax to the campaign, the top three being separated by just one point having scored 256 goals among them, with the prospect of a play-off to decide the champions remaining alive until the final few seconds of the term.

As it was, United's victory ensured that they were the ones flying the flag. Yet while the venue of their coronation made it even more special, their succession only came after a fraught finale in front of 29,106 supporters wedged into Dens. The game had started better than the league leaders could ever have imagined, Ralph Milne marking the weekend of his 22nd birthday with a goal so breathtaking that it has become immortalised in song. Fed by Paul Sturrock on the edge of the centre circle, the winger wriggled past Stewart McKimmie and ambled forward before glancing up and chipping the ball nonchalantly over the head of goalkeeper Colin Kelly from 25 yards. It was, in the words of the chant, Happy Birthday Ralph.

Within 11 minutes, United were two ahead. David Narey was fouled and, although Eamonn Bannon's penalty was saved, he reacted quickest to lash in the rebound. "I was never nervous taking penalties," the winger recalled. "But I remember having to wait a few minutes to take it and I made the mistake of changing my mind and I got lucky."

Regardless of such fortune, the two-goal advantage appeared to confirm that the title was heading to Tannadice. Not yet, though. Iain Ferguson – who would score a winner for United at Camp Nou four years later – rifled a shot past McAlpine before the interval to haul Dundee back into the game and set United nerves jangling. Indeed, it became so nervy that even the phlegmatic goalkeeper was panicking. "The last 10 minutes, I kept on shouting to the dugout 'how long to go?' because we were hanging on," says McAlpine. "The final few minutes seemed like an eternity."

For Bannon, the tension even affected his celebrations. "You see players go mental after they win leagues but I was very subdued," he says. "We didn't play well and it was a real anti-climax for me. I just felt shattered."

That it took until the last few moments of the campaign for such doubts to creep in were a consequence of United thinking their title hopes were over after losing 2-0 away to Celtic in April, the defeat leaving them three points off the pace with another trip to Parkhead pending. "At that point, I honestly believed the league was beyond us," McLean later admitted. The manager's concern was that the lack of depth in his pool – only 14 players made more than five appearances – would be their undoing but instead United's shallow squad roused themselves, winning their final six matches.

Each of those games, including three consecutive 4-0 wins ahead of the decider, were vital but one stands out. United returned to Glasgow and secured a surprise 3-2 victory, despite the dismissal of Richard Gough. "That was the turning point," insists Bannon, even if his recall of the game is sketchy. "I remember the pitch being like a beach, big Goughie getting sent off and Ralph scoring a great goal . . . did we get a penalty?"

They did. And he scored it, adding to Hegarty's opener and preceding another virtuoso effort by Milne, who had also scored twice before being sent off in the win at Pittodrie a few weeks earlier.

The triumph in Glasgow moved McLean's men within a point of Celtic and they went top for the very first time that weekend, towsing Kilmarnock while Celtic were losing to Aberdeen, who were four points behind with two games in hand. The failure of Alex Ferguson's side to win at Easter Road seven days later, coupled with a thumping United win at Morton, ensured it was in the Tannadice side's hands but, still, it was only in that second half at Dens that the nerves kicked in.

For the superstitious McLean, the anxiety had started weeks earlier, building to such an extent that he refused to arrange any official celebrations before the title was won. Hegarty recalls wandering back down to Tannadice for a drink in the boardroom, before attending a club function in Coupar Angus, then retiring to Frank Kopel's house until the early hours.

Bannon was there, too, but still nurses a sense of regret that "wee Jim was too miserable to rent a place" for a proper party. That said, Sturrock has a hazy memory of the manager, dressed in his pyjamas, kicking him out of his house at 7am; something McAlpine also remembers. "Ken this, I couldn't tell you most of what happened because we had a right few bevvies," he says. "God knows where we went but I know we were in wee Jim's house for a while and Luggy reckons he was given a swearing."

The party continued at Station Park the following afternoon, McLean having committed to taking a strong team to play a benefit match for Billy Bennett and John Clark. Almost every member of the league-winning side played some part despite many of them being barely able to stand, never mind run, with the injured Sturrock sent to source pies and pints. "I don't think I played," says McAlpine. "But I was so bevvied that I've no idea. I do remember wee Jim asking at half-time if anyone wanted to come off and everyone put their hand up."

Bannon was absent, nursing his own hangover while being kicked up and down Easter Road by John Brownlee in a testimonial for Jim McArthur, but Hegarty remembers surviving the 90 minutes. "I dunno how we got on . . . but I don't think we did particularly well," he says. "Just like the game the previous day, it seemed to go on for ever."