Shakes Mashaba made three changes from the team that won 3-1 in the first leg as Thulani Hlatshwayo, Dean Furman and Mpho Makola came in for Anele Ngcongca, Andile Jali and Thulani Serero.
Angola coach Romeu Filemon made eight changes to his team as he had nothing to lose. The Sable Antelopes needed to win by three clear goals to progress.
It was an unventful first half with Angola creating the better openings and Shakes Mashaba's side not offering very much going forward in a half low on quality.
Jackson Mabokgwane had a few nervy moments in goal and needed Rivaldo Coetzee to bail him out after he dropped a second cross in quick succession in the 13th minute.
Bafana's best attacking moment came in the 21st minute when Tokelo Rantie got free down the right channel, beat his man for pace, got to the byline, checked, and then crossed for Mandla Masango who could not get any telling contact.
Angola's clearest chance came in the 39th minute when Menga Dolly beat Erick Mathoho on the left side of the area and crossed, the ball bobbled loose and Fredy barged Thabo Matlaba off the ball before quickly turning and shooting, but luckily it went over the bar.
In the second half Angola kept at it and had a golden opportunity to get back into the tie when Gelson went clean through on goal, rounded Mabokgwane but then could only fire his shot against the upright from a tight angle with an open goal at his mercy.
Mashaba brought on Thulani Serero and Sibusiso Vilakazi for Mpho Makola and Thamsanqa Gabuza just before the half-hour mark. Those two players have a CAF Confederation Cup Final to play for Orlando Pirates on Saturday.
Then South Africa got some good fortune and took the lead in the 67th minute when Mandla Masango swung in a cross, Hlatshwayo headed it back across goal and Manucho Diniz turned the ball past his own goalkeeper.
Now enjoying a healthy 4-1 aggregate lead, Bafana played with more swagger after the goal as Zungu stung the palms of Dominique from long range and Rantie kept running at their defenders, albeit with not much joy.
Dean Furman, who was named man of the match, was doing an excellent job destroying Angola's potential counter-attacks as Mashaba's side kept things comfortable and started to control possession. Kamohelo Makotjo also got a run-out in the 76th minute as he replaced Zungu.
Besides a few wayward long-range efforts, Angola had one more sight of goal in the 85th minute when a corner was swung in and Mabokgwane was again caught flapping at the ball without dealing with it as a header went over the bar.
Bafana were not fluent throughout the game but in the end it was comfortable as the boys strolled to a 4-1 aggregate victory to book their place in the draw for the third round group stages of African World Cup qualifiers.
Bafana XI: Mabokgwane (capt), Hlatshwayo, Mathoho, Coetzee, Matlaba, Masango, Furman, Zungu (Mokotjo 76'), Makola (Serero 59'), Gabuza (Vilakazi 58'), Rantie
Angola XI: Dominique, Mafuta, Miguel, Gomito (Papel 71'), Diniz, Isaac, Cardoso (Bua 70'), Bastos (capt), Menga, Fredy, Gelson