Jeremy Bokila and Joel Kimwaki got the other goals as DR Congo staged a remarkable turnaround to reach the last four for the first time since 1998.
They will meet either the Ivory Coast or Algeria in Bata in Wednesday's semi-final.
After a dour opening 45 minutes, in which there were just a few half-chances, the game came alive with six goals in the second half.
Congo, who had won Group A with seven points, went 2-0 up with goals from Ferebory Dore in the 55th and Thievy Bifouma seven minutes later as DR Congo seemed to be heading for the exit.
Instead, DR Congo hit back by romping through the last 25 minutes and also hitting the woodwork twice.
Dore's opener came after he sneaked in behind the DR Congo defence to touch home a free kick from Delvin Ndinga. He might have had the second as well but his shot was smothered, with the rebound falling to Bifouma.
Yannick Blaise launched the DR Congo comeback with a speedy run down the left and a cut back that Mbokani tucked home from close range in the 65th minute.
A thunderous shot from Bokila levelled the score 10 minutes later and the turnaround was complete when a third came from substitute defender Kimwaki, who brushed home Neekens Kebano’s free kick as the opposing defence were caught static.
Mbokani made it four in stoppage time after his first effort rebounded.
"We were still believing at 2-0 but to be honest never thought we’d get four,” said coach Florent Ibenge, the last African in charge of a team left in the tournament in Equatorial Guinea.
"I thought we still had a possibility of getting back. We changed our tactics a bit and that helped us. We finished well although we also had more chances."
DR Congo had come through the group phase without winning, three draws sneaking them into the last eight.
They are former winners in 1968, when the country was known as Congo-Leopoldville, and in 1974 as Zaire but have since not realised their potential.
For the other Congo, the result was a cruel blow. "We lost composure after we went 2-0 up. We were a bit euphoric," explained their coach Claude Le Roy.
(Reporting by Mark Gleeson; Editing by Ian Chadband/Alan Baldwin)
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