The South Americans, ranked 10th in the world and heavily favoured to advance to next year's finals in Russia, had only two real chances to score a crucial away goal as home captain Winston Reid marshalled the All Whites' defence with aplomb.
New Zealand goalkeeper Stefan Marinovic made a goal-line save after a mix-up in defence and then tipped over a header from Aldo Corzo in the second half as the home team held its shape in the intercontinental playoff.
All Whites midfielder Ryan Thomas had arguably the best chance but his 85th-minute shot flashed centimetres wide of the right-hand post and the sides head to Lima dead-locked for the second leg on Thursday.
"It is a really strong result for us, big result and we are pleased with where we are at,'' All Whites coach Anthony Hudson said. "But our feet are right on the ground.
"We haven't achieved anything yet. We still want to get to Russia. All we have to do is score one goal and that puts added pressure on them.
"We are looking forward to going to Lima. This actually suits us. We are used to that type of adversity,'' Hudson said.
"We are very confident we can go there and score.''
Burnley striker Chris Wood started on the New Zealand bench after going into the camp with a hamstring injury but was subbed on with 16 minutes left as the All Whites looked for a goal.
The Peruvians, under immense pressure to qualify for a first World Cup since 1982, dominated early, with midfielder Christian Cueva and forward Jefferson Farfan causing problems for the home team's defence.
Despite its superior possession, it had only one genuine chance in the first half when Marinovic pawed the ball away centimetres from the line after a defensive mix-up with Reid.
The Vancouver Whitecaps goalkeeper was also cin action in the 63rd minute when he pushed a powerful Corzo header from a corner over the bar.
Wood forced the only real save by Pedro Gallese with his first touch before Thomas had his chance to send the crowd of 37,034 into delirium when a loose ball fell to him.
His shot flashed just wide.
"We deserved a little bit more,'' Peru coach Ricardo Gaerca said through an interpreter. "We had control of the game but couldn't score.
"The All Whites are very tough. They have a very good organisation, but we will improve.''
New Zealand defender Storm Roux will not make the trip to Lima after failing to recover sufficiently from an ankle injury.
