"We were treated a bit like rock stars," says Vicelich. "It was a novel experience for us."
The team had two security guards (both former undercover cops) escorting them around and a cavalcade of police cars that helped them through the traffic to games and training. In contrast to the class of 2013, the 1999 team enjoyed an extended build-up. They played nine games in the five weeks before the tournament, including a match against Poland (0-0), two games with African champions Egypt (1-1, 0-1) and two matches versus Oman (0-1, 2-2).
"To perform at your best, you need tough pre-tournament games, which is what we had," says Zoricich. "By the time we arrived, we were match-hardened, fit and had confidence in our combinations."
The team was based at Guadalajara, the scene of Gordon Banks' legendary save from Pele in the 1970 World Cup. The Estadio Jalisco sits 1600m above sea level - not quite the 2300m that the All Whites will face at the Estadio Azteca next month but a lung-buster nonetheless.
"We had time to acclimatise," remembers Vicelich. "We arrived in Mexico more than a week before the tournament. But it was step by step. At first, we would train for just 20 or 30 minutes, short and sharp - otherwise you would get too tired."
"[The altitude] definitely affected the flight of the ball," says Zoricich. "I remember shooting practice in the first few days and the shots were flying all over the place. It seemed to swerve, move and dip more and it travels further."
In their first match, New Zealand faced the US in front of 60,000 fans.
"It was a huge stadium and it felt like most people were cheering for us," says Vicelich. "We were the underdogs but also the US wasn't that popular in Mexico at the time."
The All Whites acquitted themselves well but lost 2-1, with a spectacular injury time free kick to Zoricich providing some consolation. Four days, later they faced Germany, featuring Lothar Matthaus, Jens Lehmann and Michael Ballack. It was a 2-0 defeat but another creditable performance.
"They suffered from the altitude in the second half and we had our chances," says Vicelich. "We finished strongly but couldn't take our opportunities."
The undoubted highlight was the match against Brazil, 17 years after New Zealand faced the South American giants in Spain. The Selecao took the lead in first-half injury time but only sealed the result through an 88th minute goal to Ronaldinho, as the All Whites defended doggedly and created several half chances.
"That match is the lasting memory for me," says Zoricich. "The Mexican crowd really got behind us. At one stage in the second half there were chanting 'Ole' every time we completed a pass. It was a special occasion."
The tournament was also Ryan Nelsen's first bow on the international stage. He had made his debut only a month before the tournament (against Poland) but was quickly into his stride, playing a dominant role in the matches against Germany and Brazil.
"He was new to the team but his potential was obvious," says Zoricich.
New Zealand didn't get a result in 1999 but managed three creditable performances - but will need to do better next month if they are to progress.
"It will be a much more intimidating atmosphere this time round but the basics remain the same," says Zoricich. "They will need to prepare well, believe in themselves and try to get plenty of bodies in the middle of the park so they can disrupt the flow of possession wherever possible. It's going to be an uphill battle [next month] but we have to believe we can get something out of the game."
