South Africa needed only 47.3 overs to reach a victory target of 217 and clinch a 2-0 series win, which takes them to fifth place on the International Cricket Council's ranking list, swopping positions with New Zealand.
South Africa had to overcome stubborn resistance by New Zealand's lower order batsmen before they could start their run chase Sunday.
It took South Africa 95 minutes to take the last four New Zealand wickets, with the left-handed Daniel Vettori hitting 60 as the Black Caps added 69 runs to their overnight total of 214 for six.
Smith and Boeta Dippenaar batted aggressively, putting on 69 in the first 14 overs before Dippenaar was caught behind off Chris Martin. Smith went on to make 68 off 80 balls with nine fours and a six.
After a poor season in which he had not made a half-century in eight previous Tests, Smith made 63 in the first innings in a match which yielded only four scores over 50.
Smith was clearly intent on finishing the match with two days to spare, reaching his fifty off 72 balls.
Then, when left-arm spinner Vettori came on for the first time in the match in the 25th over, Smith lofted him over mid-on for four and then deposited the next ball on to the grass bank beyond midwicket for six. New Zealand captain Stephen Fleming promptly took Vettori off.
Smith was out in the next over when he tried to cut left-armer James Franklin and was caught behind.
Hashim Amla and Jacques Kallis both fell shortly before tea, while AB de Villiers was bowled by Franklin soon after the interval to give New Zealand a glimmer of hope.
But Ashwell Prince and Shaun Pollock took South Africa through to only their second win in nine Tests in an extended season. They lost five out of six Tests against Australia before taking on New Zealand.
Earlier, South Africa used five bowlers as for the first time in the match bowlers failed to dominate during the morning's play.
Vettori and Jacob Oram took their seventh wicket stand to 49 before Oram mistimed a drive against Dale Steyn and was caught by Dippenaar diving forward at mid-off.
James Franklin provided more frustration for the bowlers as he and Vettori added 44 for the eighth wicket before the innings ended in a rush, with the last three wickets falling for no runs in six balls.
Franklin padded up to a ball from Pollock which cut back and hit the top of his off stump. Vettori edged a drive against Andrew Hall and was caught by De Villiers at gully after a 91-ball innings which included eight fours.
Chris Martin was out first ball when he paddled a bouncer from Hall to Amla at backward square leg.
South Africa won the first Test in Centurion by 128 runs and the second Test in Cape Town was drawn.