Skipper John Sheridan was carried shoulder high around the perimeter of the Elland Road pitch after a 3-2 victory against West Bromwich Albion secured United's spot in the top-four of the old second division and guaranteed them a place in the end-of-season lottery.
The success opened enough daylight between Leeds and sixth-placed Crystal Palace to ensure Billy Bremner's side participation in the Football League's revolutionary idea for spicing up the end of a long campaign.
It was an experimental year for the play-offs with the 19th placed side from the top division joining in along with the teams finishing third, fourth and fifth from the second tier.
The idea hadn't been warmly received by football chiefs up and down the country – in previous years the 19th place side would have been safe for another year and the team finishing third in the second division would have been guaranteed promotion.
As it was, Charlton were the top-flight outfit who were forced into slugging it out for their future while Oldham Athletic, third in the second division, were being told to compete against a Leeds side who finished some seven points behind them in the table.
Unsurprisingly, Latics boss Joe Royle was the most vociferous of the critics – demanding to know why his side should be forced into playing extra games to decide their future, but the rules were in place at the start of the season and all the competitors started on a level playing field.
Leeds had come up on the rails to qualify for the play-offs after a strong finish to the season. An extended run in the FA Cup – Leeds were eventually beaten by Coventry City in a thrilling semi-final at Hillsborough – had left United with an horrendous fixture pile-up, but Bremner's side held their nerve well.
Shrewsbury were beaten just two days after that FA Cup semi-final clash while Ipswich Town, Birmingham City and West Brom were all beaten at Elland Road.
Buoyed by the play-off qualification over 4,000 Leeds fans headed for the final day clash at Brighton when a Keith Edwards goal proved enough to ensure they signed off their league campaign on a high.
But, after a season of heartbreak and drama, the real thrills and spills were only just starting with the arrival of the play-offs matches.
While Charlton were handed a two-legged meeting with Ipswich and duly beat the fifth-placed side in the second division 2-0 on aggregate, Leeds were handed yet another double-header with Oldham Athletic.
The two sides had already met four times so far that season. The Latics won a two-legged League Cup tie 2-1 on aggregate while league honours were even with both sides winning their away fixture.
Almost 30,000 crammed into Elland Road for the first leg on a Thursday evening and the game was a tense, nervy affair. Royle's Oldham side were a well-organised outfit with a rigid defence, but equally their tally of 65 goals for the season was the best of any side in the second division.
The Latics showed little in the way of enterprise at Elland Road and another vital goal from substitute Edwards gave Leeds a 1-0 advantage to take across the Pennines for the second leg.
The return match was a Sunday high-noon affair at Boundary Park and 5,000 United fans swelled the crowd to a season best of 19,216. To add extra spice to the clash former Leeds trio Denis Irwin, Andy Linighan and Tommy Wright all lined up in the Oldham side and, with the hosts boasting a revolutionary plastic surface, the scene was set for a cracker.
Once again, nerves abounded and the pressure clearly affected the players of both sides, but it was Oldham who settled quickly and levelled the tie courtesy of a goal from Gary Williams.
With extra time looming, Latics substitute Mike Cecere popped up to fire his side ahead on aggregate and with just minutes left, Leeds looked set for play-off heartbreak.
But Bremner had his own super-sub in Edwards and while the Oldham fans celebrated, Leeds launched one final attack upfield and the prolific striker was on hand to score the most crucial goal of the season.
The clash went into extra time, but the away goal was to prove decisive and, despite finishing way adrift of the Latics in the league, it was Leeds who took a giant step towards securing promotion to the top division.
Unlike now, the play-off final was a two-legged affair for the first few seasons and six days after beating Oldham, United headed for Charlton's temporary home at Selhurst Park.
The game was in keeping with the theme of the other play-off affairs and a dour, drab contest was settled by a Jim Melrose goal in front of just 16,680.
The second leg was set for Spring Bank Holiday Monday evening at Elland Road and a full house crowd of 31,195 packed in hoping to witness a piece of history.
As it was, the edgy crowd watched another dull affair, littered by nervy mistakes and as the clock ticked down, United's hopes appeared to be in tatters.
But the Elland Road crowd hadn't banked on a Bob Taylor/Brendan Ormsby combination to save the day. Taylor was the man who stabbed a goal-bound shot past the reach of Charlton keeper Bob Bolder before Ormsby appeared on the line to force the ball home.
The roof came off at Elland Road and when extra time failed to produce another goal and with the score locked at 1-1, red-faced Football League officials were left scrambling around to come up with a solution to settle the tie.
There were no penalties and it was decided that the game would go to a replay on a neutral venue – Birmingham City's St Andrews ground.
The following Friday 15,000 Leeds fans headed for the Midlands for the do-or-die showdown with Lennie Lawrence's Londoners.
United fans took up three sides of the ground while the 3,000 Charlton fans occupied the old away section in the corner of the Tilton Road end.
Unsurprisingly, it was another dreadful game with the stakes high and with the players clearly feeling the heat. The atmosphere was one of edginess – probably more tense than any game Leeds have played in the last 30 years – and every shot, tackle and challenge was greeted with an anxious "ooh" or an "aah" by the crowd.
United lost the services of Ormsby, who later admitted he had paid a heavy price for attempting to put Garth Crooks out of the game and Bremner re-shuffled his pack.
Neither side gave an inch and as the game entered into extra time calls of "All we are saying is give us a goal" echoed around the ground from the United followers.
That request was granted during the first period when John Sheridan delivered the sweetest of free-kicks past a helpless Bolder and, to all intents and purposes, Leeds United's five-year exile out of the top division was over.
The fans partied as though it was 1999, never mind 1987 and set about roaring their heroes through the nerve-jangling second period.
But fate was to deal a cruel hand and Charlton, who had offered little in the way of a threat, somehow conjured up two goals from centre-back Peter Shirtliff to turn the tie around.
The double strike killed Leeds. The players were already running on auto-pilot and Bremner's men could barely summon up the energy to muster an equaliser. In the space of a few minutes the dream was over.
In typical fashion of that era, a handful of Leeds fans attempted to pull down the perimeter fencing, but they were shouted down by the majority who, quite simply, felt as low as they had ever done watching a football match.
The final whistle was greeted with devastation and disbelief. The Charlton players trotted to their corner to celebrate with their travelling fans while the Leeds players lay on the pitch, tears aplenty.
"We'll support you ever more" boomed around St Andrews as the United fans put on one final act of defiance before heading back to the M6 to reflect on what might have been.
The Football League patted themselves on the back on a successful experiment and immediately drew up plans to make the play-offs a permanent fixture while, once the tears had stopped, United fans ruefully admitted that promotion may have been a step too far.
The feeling, though, was that the play-offs can be a cruel, cruel way to end your season. Unless, of course, you are successful.
It was an experience that very few who were at Birmingham that night would want to repeat, but here we go again, hoping for a very different outcome.
Read Dewsy in the YEP Monday to Saturday