That would have only been possible if the Super Eagles were consistent in their pattern of playing a more attacking game at the onset of the match to score more goals in the first 30 minutes, before a defensive game, rather than playing a defensive game before attacking at the die minutes of the match. Because if we are to have a look at the Head-to-Head review of the past 13 matches between both teams, Nigeria has won 7 times, South Africa won 2 and both played draw 4 times. Hence, when Nigeria is playing with South Africa, it's always best bet on either "Nigeria to win or draw"
You are right on your observations of how Nigeria plays. Truthfully, it seems like they don't know how important the game is and chose the option of defense from the start. South Africa are understandably bitter rivals to Nigeria and as such will do anything to make things difficult which they did. If you ask me, I'd say the Eagles take international games less important than they do at their clubs.