It appeared as though South Africa would rue Andile Jali's missed penalty when Ahmed Musa's excellent strike put Nigeria into a 1-0 lead with five minutes left on the clock.
But Zungu pounced to earn a share of the spoils in the fourth minute of additional time in Nelspruit.
Shakes Mashaba's side started the brighter and Zungu forced Daniel Akpeyi into a fine fingertip save with an accurate drive from the edge of the penalty area after good work by Thulani Hlatshwayo.
The hosts continued to probe and Tokelo Rantie's excellent work rate was causing problems for the Nigeria defence, the striker providing one particularly menacing cross that Sibusiso Vilakazi glanced wide of the left-hand post.
Nigeria's attacks had largely been repelled by the home team, although Aaron Samuel's left-footed bending effort beat Itumeleng Khune in the South Africa goal but went narrowly wide.
The visitors were dangerous on the counter-attack after the break, but it was South Africa who fluffed their lines with the game's best chance in the 61st minute.
Thulani Serero was chopped down in the penalty area by Godfrey Oboabona and from the resulting spot-kick Jali saw his effort saved by Akpeyi.
It appeared as though that would be a costly miss in the 85th minute when Musa cut in from the left-hand side before bending his strike into the far top corner.
