Woodward, speaking to zurichpremiership.com a day after his team's 25-6 victory over the Boks in their 2003 RWC Pool C clash in Perth, said South Africa remained a world-class outfit.
All they now have to do, is believe in their own abilities.
"They were excellent," Woodward said of the Boks' performance against England, the No.1-ranked team – according to the Zurich World Rankings – at the weekend.
"[And] there was no nonsense," he added, in reference to the previous meeting between the two teams, at Twickenham last November, which was marred by foul play.
"The South African are a world-class rugby nation and have outstanding players. I think that they did themselves credit.
"I have always thought in the back of my mind, and I have never said this publicly, that whoever lost that game [at the Subiaco Oval] is not out of the running [for the World Cup].
"The South Africans can have a really good go at the All Blacks in the quarter-finals, if that is the game. They have to believe that they can win.
"They will be down today [Sunday], but no more than that. Everyone has said that whoever lost [in Perth] would have to face the All Blacks – almost like it is a foregone conclusion.
Well, I don't think that the All Blacks are setting this tournament alight at the moment and the Springboks have got to go down to Melbourne and believe that they can win … which they can."