An inexperienced Super Eagles outfit looked to be heading for victory when Ahmed Musa beat Itumeleng Khune with a fierce drive into the top corner in the 85th minute.
However, Mamelodi Sundowns ace Zungu capped off a fine individual display when he pounced from close range at the death to earn a deserved share of the spoils for Ephraim Mashaba's men.
Bafana Bafana, though, will still feel they missed a chance to record a rare win over the west Africans as they looked the more dangerous side for much of the tie, and squandered a penalty through Andile Jali.
The hosts, who beat Swaziland 3-1 in midweek, started brightly, as Zungu had an effort tipped over six minutes in by debutant goalkeeper Daniel Akpeyi.
Moments later Akpeyi scrambled across his goal to field a header from Man of the Match Mulomowandau Mathoho off a corner.
Nigeria, who lost the services of Kenneth Omeruo early on through injury, saw plenty of the ball but battled to make inroads in the final third, while Bafana were threatening on the counter.
Tokelo Rantie nearly struck midway through the first stanza after being played in by Zungu but his shot in the box was brilliantly blocked by Leon Balogun.
At the other end, China-based forward Aaron Samuel and Chima Akas fired efforts from range on Khune's goal without really troubling the Kaizer Chiefs goalkeeper.
Rantie was put into space down the right close to the interval but his cut-back was just behind the onrushing Thulani Serero.
Bafana had a great chance to take the lead just past the hour-mark when the tricky Serero tumbled in the box under a challenge from Godfrey Oboabona. Jali's penalty, however, was kept out by Akpeyi, with Nelson Ogbonnaya almost netting an own-goal when clearing as his wild kick struck the upright and went out.
Soon after Akpeyi foiled a shot on the angle from Rantie, while Oupa Manyisa dragged an attempt wide in the latter stages after combining smartly with Serero.
Mashaba later brought on Lehlohonolo Majoro and Sibusiso Khumalo in place of Rantie and injured left-back Thabo Matlaba, before Musa stunned the home supporters with a telling strike from outside the box for his 10th international goal.
Zungu, though, hit back in the third minute of optional time when he swept the ball home after Majoro's attempt was parried into his path.