The aircraft - which was carrying 118 passengers - then circled over Dunedin while the crew attempted to fix the fault, without success, she said.
The decision was then made to divert to Christchurch International Airport, where its wider runway meant "it didn't matter that we couldn't steer," she said.
"There was a round of applause when the plane landed in Christchurch safely and with no drama," she said.
The aircraft was then towed to the terminal building, where passengers were offloaded and arrangements made to fly them to Dunedin on another aircraft later last night.
Ms Harwood was full of praise for the flight crew, who were "very good".
"They were all very calm and very professional and everything - no drama really.
"It's mildly inconvenient but oh, well. These things can't be helped, can they?"
An Air New Zealand spokeswoman confirmed the flight had been diverted to Christchurch because of an "engineering issue", and apologised to customers "for the inconvenience caused".