One passenger, Deborah Sylvester, 34, said it felt like the steep run on a rollercoaster.
"It was very sudden. Both going down and back up were steep. You got that feeling where you lost your stomach.
"I closed my eyes and hoped for the best. I was holding on to the chair in front of me very tight. You knew this was more than a bit of turbulence."
She said the pilot explained over the intercom that a small plane had been flying at an unsafe altitude.
"His words were 'We were on a path to collision'," she said. "I didn't see how that could have ended well, but he sounded very calm and I think that helped make people feel better.
"I'm just very grateful for the technology that picked up the other plane."
Her husband Andrew Sylvester was watching a music video of Bon Jovi's Living on a Prayer when the plane throttled suddenly out towards the sea for about six seconds.
"The climb back up was pretty solid. The engine was working hard," he said.
"The wife absolutely freaked. Everyone was looking at each other. No one was sure what was going on."
He added he was impressed with the pilot, who seemed "cool, calm and collected".
The A320 and the small craft were within range of the air traffic-control centre at the time.
Lew Jenkins, group manager of traffic-control company Airways NZ, believed the planes had not come within the 150m vertical distance prohibited under aviation law.
"It was looking to being a potential safety event," he said. "At this point, we don't believe there was a breach."
Airways NZ will begin its investigation tomorrow.
In a written statement, Air New Zealand spokeswoman Tracy Smeaton said the A320 was on approach to Auckland International Airport, descending through 3000 feet, when a cockpit indicator detected a smaller aircraft close by.
She said the aircraft then lifted while circling to avoid the other plane. The go-round could accentuate the "feeling of change" for passengers, she said.
"The pilot applied thrust to climb 1000 feet higher to ensure adequate altitude was maintained between the aircraft," Smeaton said.
"The aircraft circled to recommence the approach and land."
Civil Aviation Authority spokeswoman Emma Peel said Air New Zealand, Airways NZ and the pilot of the light craft would be required to notify the authority about the incident within 12 days.