The team of tunnellers, including Whittaker, eventually found a small group of students trapped under a beam.
Two bodies had to be removed before they could rescue one student who was trapped by her ankle and another who was trapped by his head.
A third student could not be freed until a civilian doctor performed an amputation through an access hole from above.
Whittaker's death has been described as a complete shock to family and friends.
Canterbury firefighters paid tribute to "one hell of a firefighter, one hell of a man" and his contribution to basketball was remembered by Canterbury Basketball.
"The entire Canterbury Basketball community is heartbroken... Mark Whittaker was extremely passionate about basketball, was recognised as a hero for his work as a firefighter, as well as being an outstanding father, husband, friend, son."
He is survived by wife Caroline and children Charlotte, Mason, and Lauren.
A funeral will be held in the Rangiora Chapel, Wai-mana, on Thursday, with a private cremation to follow.
Fire and Emergency New Zealand staff were invited to wear uniform and medals to the service.
Caroline said the service will be live streamed for those who can not attend.