DR Congo needed extra-time to overcome hosts Rwanda 2-1 in the quarter-finals of the African Nations Championship (CHAN).
Doxa Gikanji gave DR Congo the lead after just 10 minutes of the game at a packed Amohoro stadium in Kigali.
Rwanda equalised 12 minutes after half-time with a goal from Ernest Sugira.
Padou Bompunga found the winner in the second period of extra-time and it means DR Congo will face either Zambia or Guinea in Wednesday's semi-final.
DR Congo, who won the inaugural CHAN title in 2009, took the lead when Rwanda failed to clear the ball properly and fell to Gikanji outside the area whose fierce shot left the Rwanda keeper Eric Ndayishimiye rooted to the spot.
Nine minutes later, with the Leopards dominating, Jonathan Bolingi's shot hit the post.
Rwanda's second-half equaliser from Sugira was his third of the tournament.
He managed to get behind the DR Congo defence, which was a man short with a player down injured, and neatly finished past keeper Ley Matampi.
He had the chance for second later in the match as he beat the the Congolese defence and Matampi but his lob landed on the roof of the net.
Both sides pushed for the winner before the final whistle but it remained deadlocked after 90 minutes.
With time running out and the match heading towards a penalty shootout a cross was swung in to the Rwandan area and headed back across the six-yard box for Bompunga to head past Ndayishimiye.