It was a huge shock but the Blues were so poor at the time, the result caused barely a ripple except for manager Ron Saunders who left within days.
Since then the minnows have tried and failed against the big boys, Exeter's 0-0 draw against Manchester United at Old Trafford in 2005 the pick of the bunch.
Cup king: Milton Graham scores for Bournemouth against Manchester United
And this weekend Blue Square Premier duo York City and Barrow will attempt to kick-start the romance bus 24 years after it stalled.
York - currently third in 'division 5' - lost their League status in 2004 but know what it's like to send shockwaves through football.
They won 3-0 at Old Trafford in the League Cup in 1995 and also beat Arsenal in the FA Cup ten years earlier.
They travel to Stoke City and York boss Martin Foyle will point to the fact his side have conceded just 12 goals on the road this season while their Premier League hosts have netted just 11 times this term.
At least York have current form and a bit of history on their side.
Wrexham heroes: Steve Watkin and Mickey Thomas after their 1992 FA Cup win
Barrow were voted out of the Football League in favour of Hereford 37 years ago after 51 years of non-achievement and have made hardly a wave in the amateur ranks since.
They are now 16th in the Blue Square Premier and last year lost 2-1 at the same stage to Premier League Middlesbrough.
Barrow's main FA Cup claim to fame is having defender James Cotterill jailed when his off-the-ball punch to the face of Bristol Rovers player Sean Rigg was captured on camera in 2006.
Cotterill pleaded guilty to GBH and sentenced to four months in prison after Match of the Day aired the attack.
The Ziggers will provide a tough test for Steve Bruce's out-of-form Sunderland at the Stadium of Light, roared by a 7,000 travelling Army - four times their normal home gate.
Matt finish: Matthew Hanlan nets Sutton's winner against Coventry
Older fans of Burnley will also feel a dull ache when they travel to MK Dons this weekend.
The Clarets are back in the top flight after 33 years in exile but in 1975 they suffered a crushing third-round home exit at the hands of Southern League Wimbledon.
THE DAY TIM BUZAGLO MADE HEADLINES WITH HIS MAGICAL HAT-TRICK FOR WOKINGThe Crazy Gang went on to win the FA Cup itself in 1988 and dined at football's top table for 14 years before leaving London and reforming in 2003 - as the MK Dons.
Owen Coyle, you have been warned.
But that's what MIGHT happen. To get you in the mood for a some good old-fashioned FA Cup romance - when an unknown roofer or used car salesman appears on TV but not on Crimewatch or Watchdog - Sportsmail dredged up the ten biggest third-round shocks in history.
Hereford United 2 Newcastle United 1 - 1972 Postponed three times because of bad weather, this replay was worth waiting for. With Hereford's players suffering from cramp and trailing 1-0 to a goal by Malcolm Macdonald scored just eight minutes from time, Ronnie Radford's 35-yard equaliser sparked an Edgar Street pitch invasion soon afterwards.
Then Ricky George hit the extra-time winner to make Hereford the first non-League side to defeat a first-division team in 23 years back in the days when it was still OK to play Gary Glitter songs on the tannoy and show Jim Davidson on prime time TV.VIDEO: A Cup cracker and John Motson's first main TV match
Sutton United 2 Coventry City 1 - 1989 This last time a top-flight team have been knocked out by a non-League side. Goals from Tony Rains and Matthew Hanlan humbled a Coventry side who had won the trophy 18 months earlier and were sixth in the first division. Over 8,000 packed into Gander Green Lane - and Motson was there again.VIDEO: The Sutton winner in these highlights
Wrexham 2 Arsenal 1 - 1992 The Gunners were league champions, Wrexham bottom of the old fourth division.Arsenal had taken the lead through Alan Smith but with 10 minutes to go 37-year-old Mickey Thomas unleashed a 25-yard free-kick past David Seaman for the equaliser.The Welsh side could sense an upset and Steve Watkin popped up late on to score the winner and send their illustrious opponents crashing out.
VIDEO: Both the Wrexham goals - stop laughing Spurs fans
Burnley 0 Wimbledon 1 - 1975Wimbledon were about to embark on their remarkable journey from the Southern League to the top flight and gave a taste of what was to come at Turf Moor.
Micky Mahon stunned Burnley to grab the winner but the hero was goalkeeper Dicky Guy, who made a string of superb saves.
Shrewsbury 2 Everton 1 - 2003 Languishing near the bottom of the Football League, Shrewsbury turned the form book on its head thanks to two goals from Nigel Jemson.
He smashed home a 38th-minute free-kick and then, after substitute Niclas Alexandersson had levelled on the hour, glanced an 89th-minute header past Richard Wright to seal a famous victory. But that was the only highlight of the season for Shrewsbury who were relegated to the Nationwide Conference in May.
The biggest irony of all was that they were managed by Everton legend Kevin Ratcliffe who had captained the legendary side of the 1980s.
VIDEO: The (non) taming of the shrews
Bournemouth 2 Manchester United 0 - 1984Cup holders Manchester United fell victim to Harry Redknapp's Cherries at Dean Court. Goals from Milton Graham and Ian Thompson sent Division Three Bournemouth through - long before the days of fielding weakened sides in the cup.
Birmingham City 1Altrincham 2 - 1986The last away win by a non-league side at a top-flight club. Altrincham had a good record against League sides but could not jkoin their ranks in the days before promotion. Goals from Kevin Ellis and Robert Hopkins (own goal) won it for the minnows after Hopkins had netted at the right end.
West Bromwich Albion 2 Woking 4 - 1992Tim Buzaglo's 15-minute hat-trick at The Hawthorns shattered Division Two Baggies who had led at half time. Terry Worsfold completed the misery for Albion boss Brian Talbot.
VIDEO: The Baggies' house of cards collapses on them
Walsall 2 Arsenal 0 - 1933 Herbert Chapman's dominant team were weakened by influenza, so the manager was forced to recruit players from amateur football in order to rest his reserves.
Yes, he got players in to REST his second team - how confident was that?
Years later Arsene Wenger would adopt this tactic for every domestic cup match but on this occasion the plan backfired and the Division Three team hustled and bustled an Arsenal lineup that featured seven international players and won through a headed goal from Gilbert Alsop and a penalty from Bill Sheppard - great black and white football names.
Worcester City 2 Liverpool 1 -1959 Liverpool were in the second division, but this defeat by a Southern League club was still a shock. Worcester took the lead through Tommy Skuse before an own goal doubled the advantage. A Liverpool penalty came too late and the defeat contributed to the departure later in the year of Liverpool Phil Taylor. His replacement? Bill Shankly.