The image has been picked up by media around the world, with Britain's Daily Mail inaccurately calling the pair "great white sharks".
The paper reported it showed "Charles Darwin's survival of the fittest - or perhaps biggest - theory in action".
The shark was identified by expert Clinton Duffy as a blue shark, of about average size and a common sight around New Zealand.
Ms Grover said she first noticed the shark after a few smaller school sharks began mooching around the boat. The 27-year-old, holidaying from Melbourne in her hometown of Nelson, watched it cruising back and forth beneath the surface while out fishing with Mr Everton and his wife, Kate.
"I've never seen one in the wild," she said. "I'm quite fascinated by them."
When the school shark was hooked up and drawn close to the boat, the blue shark swam in for a closer look. "He was slowly trying to grab it. It wasn't scary-scary. It was pretty non-aggressive." After a few bites around the tail, the school shark was brought on board while the blue shark submerged. There was debate about its fate. "If we bring it in, it's going to die. If we throw it back, it is going to get eaten. We threw it back. It sank out of sight."
The shark was one of about five caught during the two-hour trip. The anglers also caught four blue cod, their initial target. Mr Duffy said the image showed the challenges anglers faced.
"It is a pretty common occurrence. It's a pretty average-sized blue shark - one of the most abundant sharks in the world."
The shark appeared to be about two metres long - about half the length of a fully grown blue shark.
He said the warmer waters were bringing more sightings. There were reports of a 300kg great white chasing dogs in the shallows near Waiuku, in the Manukau Harbour.
