Woods, the tournament host and world No. 1-ranked player, seemed in control of the event after his second-round 62. But Johnson, down four with eight holes to play, caught Woods by holing out from 58 yards from a drop area for par on the final hole of regulation.
Another par to start the playoff gave Johnson his 25th professional championship. While not courting as a PGA victory, the win boosts Johnson seven spots in the world rankings to No. 9. That pushed Brandt Snedeker to 10th and Jason Day to No. 11.
Thomas Bjorn won the Nedbank event and is lifted nine places to 25th in the rankings.
Miguel Angel Jimenez repeated as Hong Kong Open titlist, building on his record as the oldest player to win a European Tour event. He turns 50 next month.
Jimenez goes from 48th to 38th this week in the rankings.
The men's world golf rankings Top 10, listing player's name, home country and rankings points average:
1. Tiger Woods, United States, 12.34
2. Adam Scott, Australia, 10.00
3. Henrik Stenson, Sweden, 9.01
4. Justin Rose, England, 7.53
5. Phil Mickelson, United States, 7.44
6. Rory McIlroy, Northern Ireland, 6.82
7. Matt Kuchar, United States, 6.47
8. Steve Stricker, United States, 6.04
9. Zach Johnson, United States, 5.71
10. Brandt Snedeker, United States, 5.52