The Leopards, inaugural CHAN winners in Cote d'Ivoire in 2009 finished second in their group behind Gabon and will now face Group C winners Ghana in the last eight in a repeat of that final four years ago.
Gabon topped the group after also coming from behind to beat Mauritania 4-2 at Free State stadium in Mangaung.
DRC who started the night in third place with three points soon found themselves on the back foot after Burundi captain Ndikumana Selemani thrust his team into the lead after 14 minutes following a neat lay-up from fellow striker Abdoul Fiston.
The Congolese, who had earlier had a goal disallowed for an infringement and also struck the cross bar from a free-kick eventually got it right in the when double scorer Jean-Marc Makusu Mundele found the target in the 24th and 37th minutes.
After seeing his fifth minute goal disallowed for an infringement, it seemed to get worse for Mundele when his 18th minute penalty was saved by 18-year-old Burundi goalkeeper Arthur Nakaza.
Nakaza however, had no answers to Mundele's double strike, which ensured it was DRC who rose into second place while Burundi - group leaders at the start of last night's matches - slipped into third with four points.
Yet the Leopards were facing a first ever early exit from the CHAN tournament as they came into the match needing a win to qualify but found themselves trailing against a youthful Burundi side.
In the end the Congolese summoned all their experience to get the win they badly needed and take their points tally to six while Gabon finished tops with seven.
Nine goals were scored in the last of the group games with the Central African derby in Polokwane also full of end to end action as Burundi threatened to eliminate their more seasoned opponents.