Needing to defeat the visiting side by at least four goals to squeeze through from Group D on the head-to-head tie-breaker, the east Africans scored three second-half goals to succeed.
It was a multi-national triumph for 'Yanga' with Tanzanian Mudathiri Yahya, Burkinabe Stephane Aziz Ki, Zambian Kennedy Musonda and Ivorian Joseph Gnadou netting.
The most crucial goal came from Gnadou, with six minutes remaining, as it overtook the head-to-head advantage Belouizdad began the match with having won 3-0 in Algeria last November.
Victory for Young Africans also ensured record 11-time champions Al Ahly of Egypt, who beat Medeama in Ghana on Friday, also qualified for the knockout stage. Ahead of the final round in Group D on March 1, Ahly have nine points, Young Africans eight, Belouizdad five and Medeama four.
Ahly will host Young Africans in a match to decide who tops the final standings while Belouizdad have home advantage over Medeama in a dead rubber.
After decades of underachievement in Africa, Young Africans improved dramatically last season to reach the final of the second-tier CAF Confederation Cup, losing on away goals to USM Alger of Algeria.
Former champions TP Mazembe of the Democratic Republic of Congo and Mamelodi Sundowns of South Africa also secured last-eight places on Saturday.
Mazembe defeated Pyramids of Egypt 3-0 in Lubumbashi and Sundowns beat Nouadhibou of Mauritania 2-0 in Nouakchott to take unassailable leads over their Group A rivals with one matchday to come.
ASEC Mimosas of the Ivory Coast and Petro Luanda of Angola have already secured last-eight places, and Simba of Tanzania and Esperance of Tunisia are likely to join them on March 2.
Simba will clinch second place behind ASEC in Group B, and eliminate
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