Led by coach Shakes Mashaba, the national team headed straight to Heroes Acre cemetery in Chesterville upon their arrival in Durban, before heading south of the city to Meyiwa's family home in Umlazi.
They were given the rest of Monday off and would begin training on Tuesday for their match-up with the Sudanese at the Moses Mabhida Stadium on Saturday.
"It was very important for us to do this. It was a very good thing and it was befitting for Senzo," Mashaba said.
"Whenever something like this happens, the mood is always very different. Some are happy, some are sad, others are still trying to come to terms with what has happened. But as we have seen, after the whole thing [the mood] is getting better.
"I can only hope it doesn't have more psychological effects for the worse, but let's see. Hopefully it will be for the better. We'll know for sure after the first training session how everyone is."
Meyiwa was shot dead on October 26, while visiting his girlfriend Kelly Khumalo in Vosloorus, outside Johannesburg.
He was made captain of South Africa following the appointment of Mashaba in June and presided over two wins and two draws. His four clean sheets put Bafana Bafana on the brink of Afcon 2015 qualification.
Topping Group A, victory over Sudan, coupled with a loss for Congo against Nigeria, would guarantee their progress.
"I think it's going to be very important for us to win this game because it will be a befitting send-off for the late Senzo," Mashaba said.
"In saying that, we don't want to put our boys under any extra pressure to win. Let them go out there and do what they're used to doing. One other thing we have been preaching is that the spirit of our late captain prevails in the team.
"Everybody's has to have this mentality that we have to play to the best of our abilities like the late Senzo had been doing."
Three players were yet to report to the Bafana Bafana camp -- goalkeeper Darren Keet, defender Anele Ngcongca and attacker May Mahlangu. The European-based trio were expected to arrive on Tuesday.
Midfielder Dean Furman, one of those among the squad which participated in Monday's activities, said it was hugely important to pay their respects.
"It was very humbling for us to be there at the graveside today and it was really touching," he said.
"It was the first time that it really sunk in for me personally. I know some of the others felt the same way too. Hopefully on Saturday we can go out and make him proud. We want to complete the job he started and we know he'll be watching down on us.
"He was our leader, our captain and we need to do it for him."