Bond missed most of a day during which Jacques Kallis and Hashim Amla shared a triple century partnership for South Africa and New Zealand, set 531 to win, stumbled to 57 for three at the close.
Kallis and Amla put on 330 for the third wicket against a team hit by injury and illness. South Africa declared their second innings at 422 for three.
Kallis made 186, three short of his highest Test score, while Amla made a career-best 176 not out.
First innings destroyer Dale Steyn took an early wicket when New Zealand batted again and Andre Nel struck twice in his first over to plunge the Black Caps into a hopeless position.
Bond left the field after bowling four overs at the start of the day. Manager Lindsay Crocker said the injury would keep Bond out of cricket for four to six weeks and that he would fly home immediately.
Jacob Oram, who dismissed Kallis for New Zealand's only bowling success of the day, limped off with a hamstring strain midway through an over and did not return. Crocker said his condition would be assessed over the next few days.
Opening batsman Michael Papps was off the field all day with a gastric illness and spent part of it on a drip.
Crocker said it was hoped the player's condition would improve overnight although because he spent so much time off the field he will have to wait until five wickets have fallen or New Zealand have batted for 262 minutes.
Former captain Stephen Fleming, who did not field in the second innings because of a badly bruised right forearm, opened in place of Papps. He was allowed to bat because he suffered an external injury.
Kallis again fell short of a Test double century, prodding tamely at Oram to be caught behind, but when he was on 120 he became the eighth batsman in Test history to score 9000 runs. It was his 28th Test century, putting him in sixth place on the all-time list.
Kallis said he was hitting the ball as well as at any time during his career. It was his fourth century in six innings following his man of the series performance in Pakistan last month when he made three hundreds in two matches.
Daniel Vettori, Fleming's successor, rotated his bowlers without achieving a breakthrough. He had the frustration of having Kallis dropped at mid-off on 108 by substitute fielder Michael Mason. At one stage four substitutes were on the field.
Kallis said batting conditions had not been easy because the bounce was uneven, although the sideways movement of the first two days had gone. "On a wicket like that I'd have taken a hundred let alone a hundred and eighty."
Amla was the first to a century when he glanced Chris Martin to the fine leg boundary. He made his hundred off 211 balls with 16 fours.
Kallis followed in spectacular style when he pulled a rare short ball from Vettori for six. He had faced 166 balls and hit 14 fours and a six. In the next over he hooked Jacob Oram for another six. Despite his let-off in the following over, Kallis continued to attack. He raced ahead of Amla as he made his third fifty off just 52 balls with seven fours and a six.
He added another six, a pull off Martin, before falling after facing 262 balls. He hit 25 fours and three sixes.
The scoring rate dropped when Ashwell Prince joined Amla before Amla reached 150 off 331 balls with 21 fours. Amla also passed his previous highest Test score of 149 when he made his only other century against the same opponents in Cape Town two seasons ago.
Steyn struck in the fifth over of New Zealand's innings when he had Craig Cumming caught at first slip. Fleming was also caught at first slip by South African captain Graeme Smith off Nel and Ross Taylor soon followed, caught by Kallis at second slip off Nel.