It was Bafana's first qualifier in Abidjan against the Elephants, who boasted the likes of Didier Drogba, Didier Zokora, Aruna Dindane, Kolo Toure, Arthur Boka, Bonaventure Kalou and Abdul-Kader Keita in their ranks.
Bafana went on to register their second appearance at the finals but Zwane failed to make Jomo Sono's squad for the FIFA showpiece in South Korea/Japan.
However, that goal helped him move to Russian club FC Rostov the following year, while he was also part of the Bafana team that won a first COSAFA Cup with a victory over Malawi in the final.
"Scoring in that game against Ivory Coast was the catalyst because the club Swallows was financially constrained," the 43-year-old Zwane tells KickOff.com.
"It is the explanation I got from the club at that time. They were forced to sell some of their stars so they can survive.
"So the only player they had to sell was me. Fortunately Rostov were looking for a left winger. I was supposed to go to Dubai for trials and in fact they wanted to monitor me after playing that game in the national team against Ivory Coast. Swallows sent the video so I went to Dubai.
"If you remember at that time Viktor Bondarenko was the coach of Swallows and he had a relationship with them because he previously coached Rostov. So the only left winger they saw at that time in the country was me and the move made a huge difference financially in my life. Although there were other issues but it made a huge difference to survive up until now.
"We had 'Makhokhoba' [Lucas Seboni], we had Gary McNab, Warren Lewis, Jabulani Mendu and when I left Swallows I think we were number one on the log table. We had the best quality squad. I remember my last game was against Orlando Pirates in Rustenburg and the late Lesley Manyathela scored in the first half.
"Before the second half started Leon Prins came storming in to our changing room and at Swallows bonuses at that time were accumulating. When you win we used to get R1500, R2000 on top and so on and so on.
"Leon Prins in that game said, 'You know what, if you guys win this game I'll give you each R5000'. When the second half got underway the first goal was scored by Jabulani Mendu. Michel Babale equalised and I think that was the last game Babale was in goals for Pirates. Serious.
"The second one was the corner and Pirates failed to clear their lines. It was scored by Lucas Seboni and we beat Pirates by 2-1."
Meanwhile, Zwane says his mom was pregnant with him for 15 months as opposed to the usual nine before giving birth at King Edward Hospital in Umbilo.
"It is the way it happened. I was born on the 10th of January. When it came time to get birth and she wasn't able to. It was in such a way no one knew what was happening. At that time she was staying at M section in Umlazi," Zwane says.
"Back then cars were scarce and not as many as they are now. Luckily, there was a father who was looking after my mother and he used to take her at King Edward Hospital when she was in severe pain. When she goes to hospital the nurses used to say, 'Her, she's not here to get birth, she's just visiting'.
"It went pass 11, 12 months, 13 months, and when 15 months started she went to hospital and nurses also said, 'Oh it's her, don't worry, she normally comes here to visit, she's not here to get birth'. She stayed and she felt 'this time I'm giving birth'.
"She pulled the bedding on the floor and she heard the baby crying and it came to the doctor's mind that she's really giving birth. Maybe it is the reason why I'm the person I'm today. I'm an honest person."
The former Manning Rangers forward came back to South Africa in 2005 to play for Golden Arrows until 2006. He then returned to Swallows before joining AmaZulu in 2008.
He retired in 2010 when Usuthu lost the Nedbank Cup final under Neil Tovey to Bidvest Wits at FNB Stadium.
He was then appointed AmaZulu team manager in 2013, but left the position earlier this year when the club was in the NFD prior to buying Thanda Royal Zulu's topflight status.
Zwane says an unhealthy working environment led to his exit amid claims he was failing to deliver on his mandate.
"I know the senior journalist who was used. I don't want to divulge his name. They used him to write every day about me," Zwane says.
"They got that information from one of the club's officials but that journalist was not the one who was writing, but he used to be a messenger and tell the other journalist in the same paper to write 'this is what happened today and this is what happened today, this must come out in the newspaper today'.
"My question is, since I'm gone, those things that they had a problem with, are they not still there? Because I can tell you now those things are still happening. One senior player told the ultra fans that the new coach [Cavin Johnson] is not playing me, he's not a good coach.
"This player has been phoning fans to come to visit him in his house and tells fans to hurl insults to Johnson during the games, why a certain player is not playing.
"How will the club moved forward? How will the coach have full access to his players? I love AmaZulu so much and I'm not bitter of how I left. Those fans were making noises to Johnson, 'Where's this player? Where is this player and why you are not fielding him?' It's sad."