Rutherford's father Ken captained New Zealand in the 1990s, the same time Latham's father Rod appeared for his country.
Left arm spinner Martin, 32, toured South Africa earlier in the season but did not get a chance in either test.
The absence through a thumb injury of Martin Guptill means two new openers will be needed for Dunedin.
Fulton, 34, last played for New Zealand in 2009.
He, too, was in South Africa but injured a knee and returned before the two tests. He still has some issues with the knee but coach Mike Hesson is confident they won't prevent him playing in Dunedin.
Latham, who has played ODIs and T20 internationals, impressed for the New Zealand XI in their T20 games against England in Whangarei and is rated among the more talented young players coming through. However he has spent little time at the top recently.
Rutherford has played against England more on this tour than any other player. The Queenstown game will be his eighth appearance in nine matches.
Rutherford and Latham are effectively batting for one spot in that game, and Hesson confirmed today Rutherford has the inside running to partner Fulton.
Hesson confirmed he and national selection manager Kim Littlejohn thought hard about promoting wicketkeeper BJ Watling back to the opening role, but his strong numbers since moving to the middle order mmitigated against that.
Prolific Otago opener Aaron Redmond, who has scored more than 900 Plunket Shield runs this season, but has been unwanted by the national selectors since 2008, was also considered.
"We could have gone for a really experienced pair for the first test (Redmond and Fulton) but felt with Martin Guptill's injury it was an opportunity to expose Hamish, who has averaged over 55 in the last two seasons of first class cricket.
"He has a temperament which suits the longer form of the game and he's a strong character."
