The 20-year-old Smith reached his hundred off just 93 balls as West Indies, requiring 441 to win, reached 354 for five when South African captain Graeme Smith gave up hope of victory with five overs remaining.
Despite Smith's heroics, the draw means South Africa have an unassailable 2-0 lead in the four-match series.
Smith finished undefeated on 105 and, with Brian Lara (86) and Ramnaresh Sarwan (69), frustrated South Africa on the final day.
However Smith's innings was all the more remarkable in that it came when West Indies were precariously poised with their senior batsmen all back in the pavilion.
The young Barbados all-rounder did not even have a first-class fifty to his name before the match but became the first West Indian to score a century on debut since Basil Williams against Australia in Guyana in 1977-78.
Showing few nerves, Smith carved the South Africa attack to all parts, his most memorable shot a square drive for six off fast bowler Makhaya Ntini while sinking to his knees.
His innings came after Lara and Sarwan had defied the South African attack for over three hours in the first two sessions, putting on 156 runs for the third wicket.
CRACKING PACE
In marked contrast to his first innings hundred, Lara began at a cracking pace, reaching his 50 from just 58
But he fell to the fast bowling of Andre Nel when he attempted a pull shot and edged through to wicketkeeper Mark Boucher. His 86 came off 138 balls and included 14 fours.
Boucher's catch to dismiss Lara lifted the South African wicketkeeper into third place n the list of Test dismissals by a wicketkeeper with 271. He is headed only by Australians Ian Healy (395) and Rod Marsh (355).
Sarwan struggled with his timing from the start and had to work for every run until he was out shortly after tea, fending an Ntini bouncer to gully. His 69 came in just over four hours off 169 balls with seven boundaries.
When Wavell Hinds was bowled off an inside edge by Shaun Pollock for 25, South African tails were up, but Smith's astonishing run spree quickly changed the tempo of the final session.
Earlier, Ntini struck twice in the first hour to remove both West Indian openers.
Darren Ganga went first, caught behind by Boucher for 10 when he attempted to hook an Ntini delivery from well outside off stump and top-edged through to the South African wicketkeeper.
Chris Gayle (32) followed when he attempted to turn a full delivery from Ntini through the leg side, the ball flying off a leading edge to Herschelle Gibbs in the gully.
