DR Congo looked set to bow out when Ferebory Dore and Thievy Bifouma put Congo in command of Saturday's quarter-final at Estadio de Bata, but Florent Ibenge's men responded from two down with stunning effect.
Mbokani pulled a goal back and Jeremy Bokila made up for wasting several chances by equalising, before Joel Kimwaki came off the bench to head DR Congo in front for the first time eight minutes from the end.
The lively Mbokani then added a fourth goal to seal the victory, as DR Congo won for the first time in the tournament to move into the last four.
Yannick Bolasie had an early chance to put DR Congo in front when the Crystal Palace winger cut in from the left but failed to hit the target with a dipping strike.
Congo were living dangerously and Bokila should have done better when his tame finish was saved by Christoffer Mafoumbi after Cedrick Mabwati had cut the ball back for him 15 minutes in.
Gabriel Zakuani was well positioned to block Arnold Bouka Moutou's strike at the other end, then Bokila lacked conviction when his weak effort was easily dealt with as DR Congo continued to probe but lacked a cutting edge.
Congo striker Dore almost punished DR Congo for their wasteful finishing when he let fly with a rasping free-kick that flashed just over the crossbar, and Bokila was narrowly off target just before the end of a goalless first half.
Bokila remained in the thick of the action at the start of the second period as his venomous close-range effort bounced down off the crossbar with Mafoumbi beaten.
It was Congo who took the lead 10 minutes after the break, when Delvin Ndinga floated in a set-piece and an unmarked Dore applied the finish from close range.
DR Congo responded and they were denied by the woodwork again when Cedric Makiadi's free-kick struck the crossbar, but more poor defending ensured they fell further behind after 62 minutes.
Thievy was the man to benefit on this occasion, with Jean Kasusula giving the ball away and then unable to keep out the striker's finish after Robert Kidiaba had saved Dore's initial attempt.
While DR Congo were vulnerable at the back, they continued to threaten going forward and they pulled a goal back three minutes later.
Bolasie was the architect, pulling the ball into the path of Mbokani, who halved the deficit from six yards.
Bokila should have equalised soon afterwards when he drilled a shot wide of the far post, but the momentum had shifted.
The equaliser came 14 minutes from time when Bokila struck a shot that Mafoumbi could only palm into the roof of the net.
Congo were then stunned when Kimwaki stepped off the bench to head home a free-kick eight minutes from time, and when Mbokani added fourth goal to complete the stunning turnaround, DR Congo progressed to the last four for the first time since 1998.
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