The two-times winners looked like they would be pushed all the way to penalties until a stunning 119th minute winner from Adil Boulbina.
Algeria won their three group games at the tournament in Morocco, but struggled to find a way past a stubborn DR Congo side in the last-16 clash.
Former City star Riyad Mahrez, as always was a huge threat, but the North Africans found it difficult to create too many big opportunities in the first half.
SUBSCRIBE TO CITY+ TO ACCESS EXCLUSIVE CONTENT
Indeed, DR Congo’s Axel Tuanzebe went closest before the break with a towering header that drifted just wide.
Mahrez tried his luck with a second half free-kick that flew over the bar before both the Algeria captain and Ait-Nouri were surprisingly substituted.
DR Congo almost took the lead immediately with Edo Kayembe’s long-range strike testing goalkeeper Luca Zidane, who has yet to be beaten in the competition so far.
Both countries went close to winner in extra-time until, with a shootout looming, Boulbina struck – cutting in from the left wing and firing an unstoppable shot into the top corner.
Algeria will now face Nigeria in the quarter-finals in Marrakesh on Saturday 10 January at 16:00 (UK).
Exeter tickets available from just £5
Be at our FA Cup third round clash with Exeter City at 15:00 (UK) on Saturday 10 January!
A piece of history will be made in the first ever competitive meeting between the two sides as both clubs set sight on glory in the oldest club competition in football!
Tickets are available from just £5 for concessions and £10 for adults so it’s a great opportunity to see your City favourites in action.
Meanwhile, hospitality packages start at just £90 for this fixture with a range of options and experiences available!
