The New Zealanders take on Peru in their Oceania-South America playoff with the odds against them after a 0-0 draw in the first leg at Wellington on Saturday.
However, Hudson believes the pressure is all on hosts Peru, who are aiming to secure their first appearance at a World Cup finals since 1982.
“We know that if Peru loses, it will be a national disaster,” Hudson said. “We don’t have that pressure. We have a united and small but strong team that is here to win.”
Hudson said he believes that awareness of that pressure will prompt Peru to begin aggressively when Wednesday’s second leg kicks off at Lima’s Estadio Nacional.
“I expect their team to try and play very fast and try and score early,” Hudson said.
“The longer the tie stays the way it is, the more it will go in our favour. I imagine the pressure will only increase on the home team every five minutes as the game goes on.
“And because of that pressure, I think they’re going to start very fast.”
New Zealand, ranked 122nd in the world, need only a score draw in Lima to be assured of their third World Cup berth, following appearances at the 1982 and 2010 finals.
New Zealand captain Winston Reid, meanwhile, was only too happy to remind Peru of their own struggles when it came to qualifying for the World Cup.
Asked to comment on New Zealand’s poor record of qualifying for the World Cup, the West Ham defender replied: “Well you haven’t been to a World Cup for a while have you?
“Records are meant to be broken, for you and for us. So we will see.”
Hudson, meanwhile, said he expects Burnley’s Chris Wood to be ready to play after a recent hamstring problem.
“He’ll be fine. Every day that passes he has been getting better,” Hudson said.
Peru, meanwhile, will look to strikers Jefferson Farfan and Raul Ruidiaz to help provide the cutting edge in the absence of the suspended Paolo Guerrero.
Guerrero is unavailable after failing a dope test last month.
“We still have one more final and we have to give everything to get to the World Cup,” said Farfan, who plays for Russian side Lokomotiv Moscow.
“New Zealand is a team that is very disciplined tactically and in defence it does not leave any space. You have to be patient to find the space.”