There were promising signs in the first half for the Springboks as they dominated for long stages and led 16-12 at the break.
But the All Blacks stepped up a gear in the second half to score 20 unanswered points for their 16th successive win, just two short of the world record, and completed an unbeaten run through the tournament.
Lock Sam Whitelock, scrumhalf Aaron Smith and centres Ma’a Nonu and Conrad Smith scored tries for the world champions, with flyhalf Dan Carter adding three conversions, a penalty and a drop goal.
South Africa scored a 13th-minute try by wing Bryan Habana, converted by flyhalf Johan Goosen, who also kicked a penalty before limping off with a heel injury.
His replacement, Elton Jantjies, also kicked two penalties just before half-time to give the Springboks the lead at the break but this was short-lived.
The All Blacks struggled initially to handle the Springboks up front, especially in the set-pieces, and the home side successfully pinned the visitors in their own territory for long periods.
But this did not initially bring reward as Goosen missed two early penalties, before centre Jean de Villiers and wing Habana combined brilliantly and used their years of experience together to fashion a try off a lineout move, flank Willem Alberts having provided momentum as he crashed the ball up.
The experienced duo combined well again midway through the first half, winning a penalty for the Springboks, which Goosen kicked to give the hosts a 10-0 lead and leaving New Zealand with a small hill to climb at altitude in front over 80 000 hostile fans.
But South Africa then provided the All Blacks with broken-field ball, centre Jaco Taute failing to find touch from a clearing kick, and they immediately pounced. Wing Hosea Gear, chosen for this match ahead of Julian Savea who scored two tries last weekend, made the half-break, found eighthman Kieran Read in support and he sent Whitelock storming down the right touchline and reaching over for the try.
New Zealand struck again six minutes before half-time as Habana broke the defensive line for the slim chance of an intercept, allowing Carter to break free, Gear again playing a prominent role and setting up Aaron Smith for an easy run-in.
The All Blacks’ narrow 12-10 lead was overhauled by Jantjies’ two penalties just before the break, but the World Cup holders produced some marvellous rugby in the second half.
New Zealand won possession from the kickoff, fullback Israel Dagg showing dazzling skills as he broke through the line and then found Read, whose tremendous linking play saw him win the man of the match award, with an overhead pass. Nonu was on his inside for the simplest of tries.
Carter’s angled conversion put the visitors 19-16 ahead and the Springboks had a chance of levelling the scores in the 49th minute, but Jantjies hit the post with a penalty.
The All Blacks continued to capitalise on the mistakes of the Springboks and Conrad Smith took advantage of gaping holes in their backline to score in the 53rd minute.
The defence of the Springboks did improve, keeping the All Blacks outside their 22 for a long period, before Carter slotted a drop goal to stretch the lead to 29-16.
The All Blacks were cruising in no obvious difficulty even with Dagg yellow-carded for stealing the ball illegally at a ruck, and the masterful Carter had the final say with a penalty in the 72nd minute that made the final score 32-16.
The Springboks were left to rue not only the errors that led to New Zealand tries, but also the times their own attacks broke down, with Habana dropping the ball when going for the tryline five metres out and another turnover deep inside the 22 after the home side had made good progress with the rolling maul.