After drawing 0-0 with minnows Cape Verde in a lacklustre start to their campaign on Saturday, South Africa produced a much more convincing display to relieve some of the intense pressure that had built up around the home country.
Defender Siyabonga Sangweni scored his third international goal when he snuck around the back of the Angola defence and volleyed home a Bernard Parker cross to give the hosts a 30th-minute lead.
Substitute Lehlohonolo Majoro then doubled the advantage just after the hour when he latched on to a long ball from Reneilwe Letsholonyane and dribbled his way through the Angola defence before finishing neatly through the legs of goalkeeper Lama.
It was South Africa's first win in their last nine matches at the finals, a run that dates back to 2004 when they beat Benin 2-0.
They are now top the group with four points while Angola have one, having failed to score in their two encounters so far.
Morocco and Cape Verde play in Wednesday's second match in Durban.
South Africa's victory is likely to revitalise the tournament for the home nation after a limp start.
The disaffection that followed their opening-day draw against the tiny Cape Verde Islands was reflected in a disappointing crowd at the Moses Mabhida Stadium, which rapidly filled up after the start of the second half.
"We hope we get the momentum going, but we don't want to get too excited and too carried way," a visibly relieved South Africa coach Gordon Igesund told reporters.
South Africa made five changes for Wednesday's game and produced a convincing performance, dominating the midfield and creating a host of chances.
The hosts' goalkeeper Itumeleng Khune was called on to save several headed efforts from Angola captain Manucho and a strong shot from Guilherme Afonso.
Angola coach Gustavo Ferrin conceded they had been outplayed, but complained about referee Komlan Coulibaly from Mali, who he felt favoured the home side.
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