After one of the club's best-ever results in Europe to overcome Italian giants AC Milan over two legs in the semi-final, Bill Nicholson's men lined-up against fellow English side Wolves in the final, again over two legs.
The first leg, held at Molineux on May 3, 1972, went to plan as Martin netted twice - including a thunderbolt second goal - to hand us at 2-1 advantage.
The return leg was at the Lane on May 17, 1972. This time Alan, captaining the team, scored a brave header early in the tie to hand us a 3-1 advantage.
Wolves equalised through David Wagstaffe but we held on to become the first side to lift the UEFA Cup in its inaugural year.
We also became the first British team to win two different European trophies after our Cup Winners Cup win in 1963. We made history that night as well, the first British team to lift a European trophy.
The second leg was one Alan will never forget as he scored the goal, lifted the trophy and was then chaired around the pitch by jubilant fans.
As it turned out, that was also Alan's last match for us - he moved to Fulham in the summer.
Back to the first leg, and Martin has no doubt as to where his second goal on the night stands in his career.
"I remember I was getting a bit of a rollicking from Alan, he was screaming for the ball down the touchline, but I walloped the ball and it flew into the back of the net," recalled Martin, third in our all-time top goalscorers list.
"It was the best goal I’ve ever scored and the hardest shot I’ve ever hit.
"I remember thinking to myself ‘if that’s on target, it's got a chance’ and if it had been at the goalkeeper, it might have taken him in with it as well. I hit it as hard as I hit everything."
Alan admitted he didn't want Martin to shoot. "It was late in the game and as he lined it up, I shouted ‘no’ to him," he said.
"He ignored me on the overlap, and I shouted ‘you…great goal!’ I was about to give him a rollicking!
"Martin was brilliant that day, he led the line beautifully, scored both the goals and that was typical of him."
Alanwas left stranded on the pitch at the Lane after the trophy presentation - and had his own lap of hour with 5,000 fans!
"We didn’t know it was going to be Alan’s last game, so it was a wonderful way to go, to do it like that," added Martin.
Alan said: "The old cliché is, if you are going to go out, to go out at the top and I’ll never forget that – the last game I played for Tottenham, I captained and scored the goal to win the UEFA Cup."
To mark the 40th anniversary of our 1972 UEFA Cup triumph, the club has released a new DVD with extended highlights of the first leg at Molineux - available for the first time.
The DVD also includes an audio track hosted by renowned commentator Barry Davies and re-unites Alan and Martin, who talk about the victory against Wolves. Highlights of the second leg also included.
We've five copies of the DVD to give away, so to have a chance of winning, answer the following question...
Which Italian team did we knock out in the semi-finals of the UEFA Cup in 1972?
A - AC Milan
B - Juventus
C - Inter Milan
To enter the competition, send an email with your answer to firstname.lastname@example.org - you can email us directly byFOLLOWING THIS LINK...
The competition will close at 3pm tomorrow - Friday, May 18 - and we will randomly select five winners.
We will contact the winners directly by email by 5pm tomorrow. Good luck!
Editor's decision final, no correspondence will be entered into....