The Citizens defeated the Burundian side 2-1 away from home on Sunday to secure their place in the Second Preliminary Round of the competition.
City went into the second leg holding a slender 1-0 advantage from the opening match in Durban, but rather than relying on their lead, Ben Youssef's charges produced another positive performance to get the job done.
Kyle Jurgens gave City the perfect start when he opened the scoring in the first minute following a Mokone cross.
The visitors continued to threaten and were rewarded again in the 37th minute when Maseko doubled their advantage after combining with Jurgens and Sirino in a well-worked move.
Rukinzo managed to reduce the deficit after the break, setting up a tense finish, but City kept their composure to see out the match and book their place in the next round.
"It was a good two-leg performance from us. We knew what we had to do after the first leg and the players handled the two games well," Ben Youssef was quoted on the club's website.
The coach was pleased that his team maintained their attacking intent despite having the advantage from the first leg, stressing that they were determined to win rather than simply defend their lead.
"We didn't come here to sit back and protect the first-leg result. We wanted to play, we wanted to score, and we wanted to win the game, and we did that."
Ben Youssef also praised his players for how they responded after Rukinzo found a way back into the contest.
"At 2-0 we were in a strong position, but when they scored, we had to stay calm. I thought the players showed good character to manage the game and see it through."
The result represents a significant achievement for Durban City, who have made an impressive start to their maiden CAF InterClub campaign.
They will now prepare for the Second Preliminary Round as they continue their bid to make their mark on the continental stage.