A guest house driver, organised by the fellow missionaries they were to stay with, was arranged to pick them up.
"He was reliable," said Mr Grainger, who comes from a farming background. "He said: 'yes I'll be there to meet you', when the bus arrived."
As expected a man was there to pick them up, holding a sign with their name on it.
Their original driver had left, frustrated with the long bus delays and, unbeknown to them, was replaced by another man, an associate of the man posing as their guide.
The family suspects that someone on the bus alerted the kidnappers to the presence of a foreign family onboard.
The Graingers were squeezed into the back of the car when things started to go amiss.
They were told they were taking a shortcut and their windows put up for the air conditioning to be turned on.
"The roads sort of got narrower and there were no street lights," Mr Grainger said. "It was dark as. We started to go round, it seemed, like the same block. It started to look a little bit suspicious then."
They later discovered the windows were locked and the child safety locks switched on.
The vehicle stopped in an unlit lane and third man climbed into the front of the vehicle and pretended to help the Graingers out of the area. They took off again through the streets of Dar es Salaam.
Mr Grainger said that when he started asking questions, the man "just told the guys to stop the car and he turned round and said: 'This isn't a joke. This is for real. We're the Mafia and we're going to steal all your cash. If you don't do what we tell you we're going to shoot you'."
Mr Grainger said he was in "disbelief". "Would you have believed you'd been in a situation like that? I was just dumbfounded really."
The four were forbidden from speaking to each other while he took US$1100 (NZ$1312) cash and Sam's iPhone. He demanded a pin number for Mr Grainger's credit card or he'd shoot one of the children.
When Mr Grainger asked his captor if he would let the children go if he complied, he was told he was in "no position to negotiate".
"We basically resolved ourselves to the fact that we were going to be shot. It was horrible. I think if we showed some resistance it could have been a lot worse and I just kept thanking him for showing us mercy."
They were driven to an ATM, and their captor made five withdrawals of 400,000 Tanzanian Shillings ($1475). When they were eventually released, they were handed back some of their own money to catch a taxi. Still shaken from the three hour ordeal, they tried to reach the guest house but then drove directly to the airport.
Their passports had been left untouched in their bags so new flights were hastily arranged.
While Mrs Grainger's worst fears were not realised - that Deane and Sam would be shot leaving herself and Briana with their captors - news of the incident stunned their eldest son back home.
"We rang him from the airport to tell him what had happened and he went into a bit of shock," she said.
"He had thought of all the things that could have gone wrong. Like if they shot us, [a threat] which was very real, that he'd be here by himself and wouldn't see us again," she added.
Both Mr and Mrs Grainger credit their faith with getting them through the ordeal.
"God, he protected us and looked after us," Mr Grainger said. "We had people praying for us and we felt his peace and protection.
"It's a horrible feeling when you haven't got a New Zealand embassy, you can't trust the police and you've had that done to you. You feel pretty vulnerable. It just highlights how safe New Zealand is, how spoilt we are really."
Since the incident the family has been visiting a counsellor.
Mr Grainger, a farmer, has not yet rushed back into work but they plan to return to Africa someday.
Russell Hohneck, senior pastor at Riverbend Bible Church, said it had been a very traumatic incident for the Graingers and he had sat down and discussed it with them. They were a good family with Africa "in their heart", he said.
A MFAT spokesperson said the consular division was not notified about the incident and assistance had not been sought.
