Goals from debutant Relebohile Mofokeng (60') and Jayden Adams (64') secured the result, to move South Africa to top of Group C with 10 points.
Benin, who Bafana play next on Tuesday, are second with eight following their 2-2 draw with Zimbabwe on Thursday.
Speaking after the match, Broos told SABC: "It was very important today that we got the three points.
"We knew it would be a tough game and we played a team that didn't want to lose.
"We had four good chances in the first half and didn't score. We corrected some things and started the second half very well [and] immediately put them under pressure. Once the first goal went in we had done the most difficult bit.
“It (the first goal) was a bit late but most important is the victory and the three points.”
Bafana Bafana forward Percy Tau has responded to growing criticism over his recent performances and absence from the national team, insisting he still has a significant role to play in South Africa's football plans.
Kaizer Chiefs' Thabo Cele admits he is desperate to overcome his recent injuries and turn out for Bafana Bafana.
Bafana Bafana suffered a 3-0 defeat to Angola in the final of the COSAFA Cup at the Free State Stadium on Sunday.
South Africa's Bafana Bafana stormed into the COSAFA Cup final with a commanding 3-1 victory over Comoros in the semi-final at Free State Stadium on Friday evening.
