Congo looked set to advance to the last four at the expense of their neighbours when Ferebory Dore and Thievy Bifouma struck to open up a two-goal lead with just over an hour gone at Estadio de Bata.
DR Congo had spurned several chances and struck the crossbar twice, but their persistence paid off as Dieumerci Mbokani pulled a goal back and Jeremy Bokila equalised in the space of nine minutes.
Substitute Joel Kimwaki then stunned Congo by putting Ibenge's men in front and Mbokani rounded off an impressive display by completing the scoring late on to ensure his country reached the semi-finals for the first time since 1998.
"We never lost hope and confidence that we could still win the match," he was quoted as saying on FIFA's official website.
"We changed tactics and formation after we went 2-0 down because I noticed the Congo defence was getting tired.
"It was very emotional to play against a country like Congo but we wanted to go through because it is not every time you get such an opportunity,
"If we had lost to Congo, it would amount to us not doing anything at this tournament. A defeat today would have been a lot tougher on us."
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