The Herald revealed recently that the Fury camp intend to spend up to five weeks in Auckland before the fight in order to acclimatise.
"This is a national sporting event with worldwide interest, and Mr Fury is the trainer of Hughie Fury," Bennett told the Herald.
"While the decision to decline the initial application was correct according to Immigration New Zealand instruction, in this case, under section 17 of the Immigration Act 2009, I am granting a special direction to grant the visitor visa to Mr Fury."
Duco Events boss David Higgins told Fairfax it was a "sound decision".
"He's no risk. He's devoted himself to training world champion boxers for the past 10 years, as evidence with Tyson Fury defeating Wladimir Klitschko for the world heavyweight title."
Peter, also the trainer of Hughie's cousin Tyson, is a key part of Hughie's camp.
In 2013, Peter was refused entry to the USA for Tyson's fight at New York's Madison Square Garden against Steve Cunningham and was forced to watch the fight in Canada. Tyson was knocked down in the second round but won by knockout in the seventh.