Steyn scored all of his side's points as the All Blacks, who sorely missed rested fly-half Dan Carter, could only respond through an unconverted Richard Kahui try.
South Africa's success, which offered a timely boost ahead of their World Cup defence next month, ensured a winner-takes-all ending to the Tri Nations next weekend when the All Blacks meet Australia in Brisbane.
Steyn was recalled at half-back in place of Butch James and immediately proved his worth with a superb kicking display that helped the world champions open up a 15-0 lead after 30 minutes that proved decisive.
An under-strength All Blacks were without the likes of Carter as well as captain Richie McCaw and Mils Muliaina but enjoyed more possession and territory in the opening half.
Steyn's boot, however, plus some bruising home defence, ensured the hosts took control on the scoreboard.
Without Carter the All Blacks lacked the cutting edge to make good use of their dominance and his replacement Colin Slade, making his second start, had to play second fiddle to his opposite number Steyn.
Steyn converted a couple of penalties inside the opening 10 minutes before the hosts had to withstand pressure at the other end.
A scything Kahui run was ended five metres short of the line but for all the All Blacks' efforts they found themselves 9-0 behind when Steyn launched over a penalty from halfway.
Steyn's field kicking was just as vital as he relieved the pressure on his side with a touchfinder that dribbled out five metres from the line.
Slade missed the chance to get New Zealand on the scoreboard when he pushed a penalty wide and it proved costly as Steyn then kicked over from point-blank range before adding a drop goal to make it 15-0 on the half-hour.
New Zealand finally broke through, though, in the shadows of half-time with the only try of the game.
Sonny-Bill Williams' inside pass to Hosea Gear cut open the home defence before he found Kahui to race over for his first try against South Africa.
Slade missed the conversion but at 15-5 the All Blacks had at least found some reward for their possession.
But after the break it was more of the same as New Zealand failed to find the craft to find their way through a disciplined South Africa defence.
When they did Jimmy Cowan's touchdown was ruled out after Israel Dagg was ruled to have passed forward following a lightning run that was brought down 10 metres short.
Steyn kicked over the only points of the second half, a penalty on the hour, as South Africa gained a confidence-boosting win.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.