In the First Leg tie at Farrar Road, Napoli went behind to the Welsh Cup winners after 43 minutes, when 19-year-old Roy Matthews headed home a Reg Hunter cross to spark a pitch invasion.
Seven minutes after the interval, Ken Birch’s penalty made sure Bangor were the first Welsh club to win a tie in Europe.
Napoli responded with a 3-1 win in Italy. If the away goals rule had been in place back then, Jimmy McAllister’s 71st-minute strike would’ve taken Bangor through.
Instead, the play-off was staged at Arsenal's Highbury on Wednesday, 10 October 1962 - the first time that the famous old home of The Gunners had staged a competitive European tie!
In front of a 20,000-strong crowd in London, the Italians went ahead through Giorgio Rosa's goal on 37 minutes. However, The Citizens showed plenty of fighting spirit to equalise through Jimmy McAllister's 70th-minute goal to level the tie.
Unfortunately, with just five minutes left of the match, Rosa scored again to end Bangor's dreams of further glory as Napoli sealed a 2-1 win.
Bangor City players as they appeared in the Official programme:
LEN DAVIES Goalkeeper. Liverpool-born has made Bangor his home. League experience with Stoke City, joined the City from Winsford five seasons ago.
IORYS GRIFFITHS Right back. A local boy and veteran of the side. A hard relentless player, gives nothing away in a tackle.
BILL SOUTER Left back. Born Dundee, a stylish full back, since he joined the City has been the first team choice.
KEN BIRCH Right half and captain, a strongly built half back with a terrific shot. League experience with Everton and Southampton.
EDDIE MURPHY Centre half, joined Bangor from Oldham Athletic four seasons ago and is proving to be the best centre-half in non-League football. Despite his Irish sounding name is a Scotsman born in Govan, Glasgow.
BARRY WILKINSON Left half. This stylish half-back was placed on Liverpool's transfer list two seasons ago, completes a Bangor half-back line regarded as one of the best in non-League football today.
ROY MATTHEWS Outside right, a 20 year old wingman joined the City from Winsford United and is regaining the form which made Manchester City hasten to sign him on professional forms.
BRIAN ELLIS Inside right, this 22 year old Liverpool boy is the only amateur in the side, a forceful inside forward joined the City five seasons ago.
EDDIE BROWN Centre forward, another player signed from Winsford and is regarded as one of the best headers of the ball in the Cheshire League, has been on Arsenal's books.
JIMMY McALLISTER Inside left, League service with Bradford, Exeter City, Accrington and Millwall. Joined the City from Rhyl. A good ball player with a terrific shot.
REG HUNTER Outside left. An ex-Busby babe who, since joining the City from Wrexham, has begun to regain form which first took him to Old Trafford.
PHOTO: Jimmy McAllister equalises for Bangor against Napoli.
Updated 19:21 - 18 Oct 2017 by Kevin Owen