Atalanta of Italy forward Ademola Lookman scored Nigeria's only goal in the 41st minute after latching onto a squared ball in the 18-yard box from Nantes winger Moses Simon to fire a left-footer past the Angolan keeper in goal.
Up until that moment, chances had been few and far between as both sides approached the game with caution.
However, midfielder marksman Alex Iwobi found wing-back Zaidu Sanusi down the left-hand side, and the Porto man played a teasing pass for Simon, who toe-poked past the onrushing Angolan defender to set up Lookman.
The game became even tighter from that point, with the Palanca Negras out of ideas on how to break down the stubborn Super Eagles' defence. Nigeria had an opportunity to extend their lead early in the second half but failed to make the most of it
The Angolans, however, came scaringly close to restoring parity in the 59th minute when Jason Dala was sent through on goal but his effort only managed to hit the foot of the post after beating Stanley Nwabali in the Nigerian goal.
Napoli point-man Victor Osimhen thought he had doubled Nigeria's lead in the 75th minute, but his header was ruled out for offside.
The Super Eagles warded off the onslaught of the Angolans to hold out for a hard-earned victory.
Nigeria will next play the winner of the Cape Verde and South Africa game on Wednesday, February 7, 2024, for a spot in the final.