A penalty from Hosny Abd Rabou and a goal from Amr Zaki put holders Egypt through to the semi-final of the Africa Cup of Nations to meet Ivory Coast.
Hosny Abd Rabou celebrates his fourth Nations Cup goal
Abd Rabou converted his third spot-kick in Ghana on 20 minutes after Angola's Andre Macanga handled in the area.
Manucho hit back shortly after with a 25-yard thunderbolt to equalise in a scintillating game in Kumasi.
But another defensive error from Kali allowed Zaki to score when he met a cross with his chest on 38 minutes.
It was hard luck for the plucky Angolans who showed technique and tenacity for much of the game, not to mention fireworks from Manchester United's Manucho.
However, the pedigree of the champions, who have not lost in the Nations Cup since 2004, proved too strong for Luis Goncalves' men.
Mohamed Shawky unleashed a low shot from 30 yards to test Angola keeper Lama on seven minutes, though the opening period was cagey with both sides cautious and slow in their build-up play.
Egypt's Emad Moteab dragged a shot wide from 15 yards out as the Pharaohs started to increase the pressure, before going close again when a cross from Ahmed Fathi flashed across the face of goal.
Manucho's thunderbolt could not save Angola from their fate
The pressure earned Egypt a penalty on 20 minutes when Macanga handled the ball when charging down an Aboutrika free-kick from just outside the area.
With some Angolan players lucky to stay on the field after harassing the Japanese referee, Abd Rabou kept his calm to shoot inside the bottom-left corner and notch his fourth goal of the tournament.
Then Manucho demonstrated why Sir Alex Ferguson was so keen to bring the Angolan to Manchester United, when he out-muscled Sayed Moawad before sending a 25-yard screamer over a flailing Essam Al-Hadari to draw the teams level with 27 minutes gone.
But just as the Palancas Negras (Black Antelopes) were dominating play, Kali failed to clear at the near post from Fathi's cross, allowing the ball to continue across the area and bounce off the body of an on-rushing Zaki for Egypt's second on 38 minutes.
Only seconds after the start of the second half Manucho had a glorious chance to equalise once more for the south Africans when he ran onto a headed pass from Flavio, only to push his shot agonisingly wide of the far right-hand post from just inside the area.
The impressive Lama thwarts another Egyptian attack
The game was now a scintillating affair, and though both teams showed attacking creativity and intent and it was Angola who were proving the more dangerous, when Manucho again caused the Egyptian defence to fret when his 15-yard shot was saved on 60 minutes.
Then Egypt hit back when Aboutrika passed onto Zaki on the edge of the area, whose deceptive flick found Moteab in the area only for Lama to pull off a brave and vital save.
With 25 minutes left and the game finely balanced the action was end-to-end, when Moteab forced another great save from Lama with a crashing shot from half way inside the penalty area.
Egyptian captain Ahmed Hassan replaced an injured Zaki as Hassan Shehata looked to maintain the Pharaohs' lead by killing the tempo and hitting on the break, as Fathi did when he tested Lama from the right wing with a stinging 20-yard shot.
As the game wore on Angola's attacks became more desperate and the Egyptians maintained their composure to see out the game and progress to meet hotly-tipped Ivory Coast in Thursday's semi-final in what is a repeat of the 2006 final.
Egypt: El Hadari, Mohamed, Hany Said, Fathi, Moawad (Fathallah 65), Gomaa, Aboutriaka (Ibrahim Said 90), Abd Rabou, Shawky, Moteab, Zaki (Hassan 71).
Subs Not Used: Abdel Monssef, Sobhy, El Saeed, Gamal, El Mohamady, Mostafa, Shaaban, Zidan, Fadl. Booked: Moawad, Gomaa, Aboutriaka.
Goals: Abd Rabou 23 pen, Zaki 38.
Angola: Lama, Airosa, Kali, Marques, Yamba Asha, Macanga, Gilberto, Ze Kalanga (Mateus 72), Manucho, Maurito (Mendonca 46), Flavio (Edson 84).
Subs Not Used: Mario, Nuno, Machado, Loco, Jamba, Delgado, Dede, Figueiredo, Love.
Booked: Macanga, Flavio.
Goals: Manucho 27.
Ref: Yuichi Nichimura (Japan).