Straight-talking midfielder Vladimir Weiss, who shares the same name as his father and national team coach, believes the world No 33-ranked side have the firepower to account for the 78th-ranked All Whites at the Royal Bafokeng Sports Palace.
Analysis of New Zealand's 1-0 defeat of Serbia in an international friendly in Austria had been useful in preparation, Weiss said.
"We know what we can expect from them. We will obviously try to get all three points," he told the FIFA website, adding that his team were bouyed by their own 3-0 defeat of Costa Rica in a friendly last week.
"When we play we will build on the work against Costa Rica. I believe that the New Zealand match will turn out as we all want."
Slovakia, who are making their first finals appearance since the 'velvet divorce' from their Czech neighbours resulted in the break up of the old Czechoslovakia, have identified the opening match as crucial to their prospects of reaching the last 16. The other teams in the group are Paraguay and defending champions Italy.
Coach Vladmir Weiss made it clear he regards the match as one his squad should expect to win and has promised an attacking approach.
"We'll be going for a win and the three points that will get us off to a good start," he said.
"Anything less than that will makes things more complicated for the remaining games.
"New Zealand is a tough opponent but I think we have more quality in our squad."
Slovakia had an impressive qualifying campaign in which their 22-year-old captain and playmaker, Marek Hamsik, who plays for Italian Serie A side Napoli, was the standout player.
The New Zealanders will also be wary of VfL Bochum striker Stanislav Sestak and Miroslav Stoch, a tricky winger who spent four years on Chelsea's books.
Stoch, 20, has shaken off a knee problem that had threatened to rule him out of Tuesday's match and enters the tournament on the back of a fine season on loan at FC Twente, who he helped to the Dutch title before agreeing to a move to Turkish giants Fenerbahce.
Slovakia's best known player, the Liverpool defender Martin Skrtel, is set to play after recovering from a minor ankle injury he suffered last week, although there is a question mark over the match fitness of the centreback, who missed the last three months of the English season with a broken foot bone.
New Zealand captain Ryan Nelsen has recovered from an ear infection and will lead the side but vice-captain Tim Brown, who underwent shoulder surgery at the end of May, is not expected to be risked before the squad's second match, against Italy in Nelspruit on Sunday.
Coach Ricki Herbert has been using Ivan Vicelich in training in Brown's role and it seems likely the 33-year-old defender will start alongside Simon Elliott, who celebrated his 36th birthday on Thursday, in central midfield.
