Ossie started every game and Ricky featured twice as Argentina memorably toppled Johan Cruyff's highly-fancied Holland team to win the final in Buenos Aires.
The pair joined us straight after that triumph, becoming two of our most inspirational signings as Keith Burkinshaw put together a team that would win the FA Cup in 1981 and 1982 and the UEFA Cup in 1984.
The teams now meet again in the semi-finals in Sao Paulo on Wednesday for the right to face either hosts Brazil or Germany in Sunday's final.
So what was it like to play and win on the biggest stage of all?
Ossie and Ricky joined us for this special insight...
What's it like to win the World Cup?
Ossie: "It was a dream, of course, a fairytale. When you start playing football you want play for the reserves at your club, then the first team, then the national team then you want to play in a World Cup and then you want to win it. All this happened in a short period of time for Ricky and me. It was simply great."
Ricky: "You never want to stop that moment. It’s a difficult feeling to explain. You have to live that moment only to understand it."
Below: The famous ticker-tape reception from fans in Buenos Aires
Can you remember your call-up for the tournament?
Ossie: "It was a bit different for Ricky. I knew I was going to be in it because I’d played every game before the World Cup, so before the squad was named, I more or less knew I was in. In the case of Ricky, he was inured at the time and it was little more traumatic for him!"
Ricky: "It was brilliant. I said ‘what a nice game football is!"
The tournament was over two group phases, and you played your rivals Brazil in the second group stage, a crucial match that ended in a 0-0 draw, and described as a 'violent' match. What was that like?
Ossie: "Yes, it was a violent game, which was a pity. Brazil were a superb team and we knew that was the game, one of us would go through, one not. We finished 0-0. It was a terrible game of football, very violent, it was like a war out there. It’s a pity because the quality of the players was so huge, it was a pity that somehow it turned out not be a classic. It was a draw, so it all went to the final game."
Below: Ossie in action against Brazil
You needed to beat Peru by four goals to get ahead of Brazil, win the group and go through to the final. You eventually
won 6-0. That must have been incredible.
Ricky: "I always felt Peru weren’t the best defensive side, they were like Brazil but without that quality, they wanted to play and go forward. I thought it would be difficult but we attacked, we scored goals. Before the game, everyone was nervous. If we had to play Uruguay, it was difficult. Peru was an offensive side, we were an offensive side and we scored six goals."
Ossie: "To be fair, Peru hit the post early on, so if that had gone in we would have had to score five anyway and that was a tall order. Having said that, we played Peru just before the World Cup and beat them in Lima and Buenos Aires quite convincingly, so we were confident. They were a good team, but a little old. They started extremely well. They beat Scotland, the game that put Scotland out of the World Cup and that was probably the best-ever Scotland team with the likes of Kenny Dalglish and Graeme Souness. But every game they were getting worse and worse, so we were convinced it was achievable and we did that."
Below: Argentina striker Mario Kempes - scored twice in the final
What do you remember about the build-up to the final?
Ricky: "As soon as we got into the final, it was very important for Argentina and the support was very passionate when we were training, when we were going to the stadium, it was a party. I enjoyed the atmosphere, probably more than Ossie because I knew I wasn’t going to play in the final. You can look a different way when you know that. It was a big day for Argentina and for the history of Argentinian football."
Ossie: "I can remember the day well. I woke up in the morning and my knees were already trembling. Ricky was there smoking a big cigar! It was party time all the way because we’d reached the final and that was our big aim. In that way, we were a little more relaxed. But the party was for the people, not for the players. We were tense, nervous. Normally, when you play a big game at White Hart Lane against Arsenal or Liverpool for example, you are nervous but after two or three minutes, it’s another game, but not in the World Cup Final. The nerves went on and on and on. It was the most nervous, stressful game I’ve ever been involved in."
Holland had a chance to win right at the end of normal time with the score at 1-1. What can you remember about that?
Ossie: "It was Rensenbrink against our goalkeeper and he did everything right, sent him the other way but he just touched the ball with an open goal, the ball was going in, certainly and there was only two minutes left, so that was that, certainly, but somehow the ball hit the post and went out. That was a big, big relief. In the final 30 minutes, I think we were the better team and deserved to win."
Ricky: "Yes, sometimes you need the luck to win and in the last minute, we had the luck, but in extra time we deserved to win."
Below: Skipper Daniel Passarella with the trophy
How did it feel to finally receive that winners' medal?
Ricky: "I say all the time that I didn’t play many games in the finals, just two halves of football, and I’m quite happy to get the medal, it’s a great honour, but I’m not 100 per cent a winner of the World Cup. Okay, don’t misunderstand that, but Ossie played every game, Kempes, Passarella, Bertoni, I believe they have more pride in that their medals. I was a little lucky because I played two halves but I’ve got a medal and I keep that for life. It’s a good trophy to keep!"
Ossie: "It was great, a relief more than anything else. It was pure joy, pure ecstacy, really wonderful, not so much when they put the medal to me, but more the moment when the whistle went and the game was over. That was the moment all the worry went and it was real party time."
What was it like to lift up the World Cup?
Ossie: "It’s quite heavy! It’s quite nice, it was a proud moment to have it in our hands."