Haller, making his tournament debut after an injury, connected with Max-Alain Gradel's pass and fired past the goaltender in the 65th minute at the Ebimpe Olympic Stadium.
That ended a tight but open semi-final matchup, and on Sunday, the same location will play host to the title match between the Ivorians and Nigeria.
After seeming on the verge of elimination in the group stage, the two-time winners pulled off an incredible comeback, becoming the first host nation to reach the final of the Cup of Nations since Egypt in 2006.
On the other hand, DR Congo's crushing loss was a blow to their hopes of making it to their first AFCON final since 1974, when they were winners as Zaire.
Before this match, Ivory Coast's interim coach Emerse Fae had praised the team's performance thus far in the tournament, calling it "miraculous" after replacing the fired Jean-Louis Gasset following humiliating group stage results.
Ebimpe Olympic Stadium on the dusty outskirts of Abidjan hosted their first encounter since January 22, when they were humiliated and on the brink of elimination following a 4-0 loss to Equatorial Guinea.
The Elephants eliminated Senegal, the defending champions, on penalties after edging out the other three best third-place teams to reach the round of 16.
Then, in the quarterfinals, they defeated Mali, a team that had to play with ten men for the majority of the match. The winning goal came in the tenth minute of extra time.
In addition to captain Serge Aurier, Odilon Kossounou, and Christian Kouame, match-winner Oumar Diakite was sent off while celebrating his goal and is now suspended.
Brighton winger Simon Adingra—who scored the equalizer in the match against Mali—and talismanic attacker Haller, who had been out with an injury, were among the substitutes.
In the 40th minute, Haller rose unmarked in the box but inexplicably missed Wilfried Singo's tempting cross with his head. Shortly after that, Franck Kessie sent a shot crashing against the post.
After an Adingra corner, the hosts sought for the kill. With only Mpasi to beat, Haller headed onto the net roof and sent a lob wide.