Days before his second birthday in March this year Chace was diagnosed with the M7 strand of acute myeloid leukaemia, but doctors do not believe the cancer is linked to the immunisation mix-up.
Since the diagnosis Chace has suffered through several rounds of intensive chemotherapy at Auckland's Starship hospital.
A final conditioning round of chemotherapy readied Chace's body for the cord blood transplant last month but the Topperwiens, both 27, were unprepared for how severe the side-effects would be.
"He was quite sick. He was in quite a lot of pain for about two or three weeks," Mr Topperwien said.
The youngster was allergic to one of the drugs used and developed a severe rash which covered his body.
High doses of morphine used to reduce the pain made Chace's skin itchy and more drugs were used to combat that.
He put on 3kg in fluid retention and his face swelled up and turned black and purple.
"I can definitely see why the body can't handle another bone marrow transplant within a year," Mr Topperwien said. "It's scary what we've seen."
Now Chace is on steroids to promote growth of the stem cells, which had to be used instead of bone marrow because a match could not be found on a database of eight million people.
And so far it's working.
"Doctors are happy with his progress," Mr Topperwien said.
More than three weeks after the transplant Chace's bone marrow is showing crucial signs of growth and his immune system is getting stronger.
"Today he was up and out of bed and walking around the room.
"He's even been singing and doing dances."
Mr Topperwien said the transplant was not easy, nor was it a "magical fix" but he said it was his son's best chance.
He and his wife were extremely grateful for the tremendous amount of support they had received for Chace, from the colourful cards sent by school children to the money donated to a fundraising account.
"This has been the most difficult experience of our lives but we have been truly humbled by the ongoing generosity of family, friends and the wider community."
Mr Topperwien, a tradesman, and Mrs Topperwien, a University of Waikato PhD student, had given up their jobs to be with Chace.
Last month they made a public plea for help to get the youngster on a drug trial in the United States in case the stem cell transplant could not go ahead.
Mr Topperwien's father, Rod Topperwien, said $75,000 had been raised toward the overseas medical intervention but he hoped they would never have to use it.
"If we do it's a last-ditch bid. We want people to know we are very thankful. It's just one step at a time. We know he's not out of the woods yet but at the moment it's an emotional high."