Former goalkeeper and captain Meyiwa was shot and killed in Johannesburg last month, with Saturday's meeting representing Bafana Bafana's first fixture since the tragedy.
Goals from Thulani Serero - his first in international football - and Tokelo Rantie clinched victory and also confirmed South Africa's passage to the tournament proper, to be held in Equatorial Guinea next year.
Keet, who replaced Meyiwa in goal for the hosts, was understandably emotional in the aftermath of the victory.
"The verse on there [his gloves] was John 15:17, where it says, 'there's no greater love than to lay down one's life for one's friend'," he said.
"I'm emotional of course, he was a great friend of mine. I just want to pay tribute and honour him. I never got the chance to go to the grave, but I hope he's watching us from above and knows that we are thinking about him.
"I just wish he was here with us, that's all I can say, that's what makes it emotional, is that he is not here with us. We want him here as a team, but unfortunately his time has gone and we have to move on and his memory will stay strong."
Elsewhere in Group A, the race for second place between Congo and Nigeria will go down to the final game, after goals from Ikechukwu Uche and Aaron Samuel earned Nigeria a 2-0 win over their rivals.
South Africa are one of nine nations to have secured their place in the finals, alongside the likes of Cape Verde and Zambia who both sealed their progress from Group F.
Cape Verde advanced with a 3-1 home win over Niger, while Zambia were grateful to Given Singuluma's goal for their 1-0 success against Mozambique.
By contrast, Group E will go down to the wire with all four teams separated by just two points.
Ghana sit top on eight points after their 1-0 loss to Uganda, who are a point behind in second. Guinea also have seven points after Idrissa Sylla's hat-trick inspired them to a 4-1 win over Togo, who sit bottom of the group on six.
Senegal joined Group G rivals Tunisia in qualifying, as they overcame Egypt 1-0 away from home, while Algeria maintained their 100 per cent record in Group B with a 3-1 win over Ethiopia.
Malawi did their hopes of claiming the runners-up spot in that group the power of good as they beat Mali 2-0, leaving both sides level on six points heading into the final round of fixtures.
In Group D, Ivory Coast's 5-1 thrashing of Sierra Leone means they need just a point from their final game to advance, after Congo DR went down 1-0 to Cameroon.
Elsewhere, Burkina Faso and Gabon are assured of their progression from Group C. The former edged past Lesotho 1-0 away from home, while Gabon's clash with Angola ended goalless.
