كتب : Mohamed Sabe
Enyeama, who also scored during the shootout, denied Tunisia captain Riadh Bouazizi in the final shot to win 6-5 on penalties after both regular and extra time ended in a 1-1 draw.
Nigeria snatched a 5th minute lead through striker Obinna Nsofor while Tunisian defender Karim Hagui headed home the equalizer four minutes after restart.
The Super Eagles will face the winner from the last quarter-final match between Cameroon and Ivory Coast later on Saturday.
The semi-final will take place in Alexandria on Tuesday.
Ziad Jaziri missed the first chance of the game as early as the 4th minute when he tried to chip the ball over Enyeama who responded with impressive agility.
Ten minutes later Tunisia were awarded a penalty-kick after Jaziri was allegedly brought down by Joseph Enakarhire.
Defender Jose Clayton stepped up to take the resulting kick only to be denied by Enyeama.
The Nigeria guardian pulled a series of emphatic saves before being beaten by Hagui who snuck behind the defense to head home from Bouazizi's cross in the 49th minute.
Both sides continued to threaten each others' goals but failed to break the deadlock, leading the game to a shootout.
Enyeama made three saves as Nigeria came from behind to win in the shootout.