You can often save hundreds of dollars this way. Your task is to find a good agent and a good deal. Official fares are often so high that planes can't be filled, so airlines arrange deals with wholesalers to clear their inventory.
Most wholesalers are legitimate, a few are bad apples.
In the US Big city newspapers have Sunday travel sections that will often list ads from travel agents. They are not likely to have the very lowest fares, but it's a good place to start. Getting a good fare involves a bit of phoning. It all depends with what airlines that agency has deals. Air fares from the US to NZ are likely to be higher for the foreseeable future, since the number of carriers serving those routes has declined in recent years.