The defending champions scored four tries to two against the competition's previous leaders, who lost hooker Bismarck du Plessis two minutes after half-time for his second yellow card for a second dangerous tackle.
But the All Blacks themselves finished with just 13 players after skipper Kieran Read (tackling a player in the air) and inside centre Ma'a Nonu (professional foul) were sinbinned in the last 10 minutes.
Read, standing in as skipper for the injured Richie McCaw, had earlier grabbed two tries, while Nonu's deft kicking was responsible for the field position for two of the touchdowns.
The result meant the All Blacks maintained their record of not having lost at Eden Park since 1994, and not against the Springboks at the ground since 1937.
But the victory came at a cost, with five-eighth Dan Carter going off in the 16th minute with a shoulder injury after an incident that led to du Plessis' first yellow card.
Just as he received a pass, Carter was hit in a big tackle and stayed down.
The challenge led to a brief melee and when the dust settled, French referee Romain Poite sin-binned du Plessis for what was ruled a no-arms and high tackle.
Du Plessis came back to score a try, but his expulsion with the score at 17-10 made it tough for the Springboks.
The All Blacks took almost immediate advantage with Read scoring his second try after an attacking scrum.
The All Blacks' bonus point touchdown came 13 minutes from time when flanker Sam Cane forced his way over.
But South Africa had the last word, replacement back Pat Lambie dotting down with six minutes to go.
Earlier, the All Blacks made a flying start in front of a sell-out 48,000 crowd, with Read scoring after three minutes from a lineout.
Then, with South Africa a man down, Carter's replacement, Beauden Barrett, made a big break that led to lock Brodie Retallick, one of the night's outstanding performers, nabbing his first Test try.
The Springboks replied through du Plessis after backing their attacking maul.
Down 14-3, they turned down a handy penalty attempt and the decision to go for the lineout paid dividends as they drove the hooker over.