"She is a fit and stubborn young woman and we know she is getting the best care.''
Two other women, aged 20 and 21, remain in Rotorua Hospital in a stable condition.
A hospital spokeswoman said the parents of one of them had also arrived in New Zealand.
Students at Boston University held a candlelight vigil and remembrance on campus yesterday to pay tribute to their friends.
The university's Facebook page is full of messages of condolence and grief, both from the United States and New Zealand.
Jan Crosthwaite, the Dean of Arts at the University of Auckland, which was hosting two of the students before they died, said: "I extend deepest condolences to the families, friends, classmates and teachers of the students from Boston University so tragically killed in last Saturday's accident, and our wishes for a speedy recovery to those hurt in the accident.
"Our thoughts are especially with the students' families and friends in the United States at this sad time.''
Kizito Essuman, president of the Auckland University of Technology's (AUT) student union, also extended the the university's sympathies.
"We are saddened by the news and on behalf of AuSM; I would like to extend our heartfelt sympathies and condolences to Boston University, relatives, friends and the loved ones of the deceased. Our hearts are with you in this time of sorrow and so are our thoughts and prayers during this tragic time.''
Austin Brashears was on an exchange programme with AUT as part of an international study abroad programme.
Prime Minister and Tourism Minister John Key told TVNZ's Breakfast programme that New Zealand could do more to prevent tragic accidents involving foreign tourists.
"It's a great tragedy, these things can happen when you've got international tourists on your roads, but obviously it's a great tragedy and our sympathies go out to the families.''
Mr Key said getting the best information out to overseas visitors was important so he had commissioned a study in 2009 into whether there was enough control and regulation of the tourism sector.
"We're not a Government who likes to put a lot of regulation on sectors; we will try to get them to operate freely if we can.''
Police said early indications were that the vehicle drifted into gravel then over-corrected, causing it to roll and throwing several of the students onto the road.