Michel Dussuyer’s side will face Ghana on Sunday following the draw at a Malabo hotel.
Guinea and Mali had finished level in Group D after they drew all three pool matches 1-1.
It is the first time lots have decided a team’s qualification in the tournament since 1988, when Algeria profited at Ivory Coast’s expense.
This time, Ivory Coast finished top of Group D in Equatorial Guinea after beating Cameroon 1-0 – the only match in the group not to finish in a 1-1 draw.
Meanwhile Caf has said the system to end the drawing of lots to separate teams that finish level in tournament groups is being looked at by the Confederation of African Football.
One representative from Guinea and Mali took part in Thursday’s draw, which involved selecting balls from a bowl.
Mali’s football association president Boubacar Diarra went first and pulled out the ball that placed them third in the group.
With Diarra in tears, Amara Dabo, financial director of the Guinea sports ministry, then drew the ball that confirmed his side in second place.
Dabo said: “The god of football fortune has smiled upon Guinea after this hard long journey.”
While any potential rule change has come too late for Mali, Binyam believes it may have been removed by the time the next Nations Cup takes place in 2017.
“The decision of the agenda is not mine but I think it’s a matter of concern for members of both the organising committee and the Caf executive committee,” the Cameroonian told BBC Sport.
“Regulations are not static, they are dynamic. We will find a way of improving the criteria to make them be decided by actions on the field.”
Binyam mooted a variety of options – from the number of shots through to the amount of ball possession – but indicated that any solution was a long way from being confirmed.
Instead, the priority is to ensure that the drawing of lots, which took place for the third time in Nations Cup history, does not happen again.
The most recent occurrence was in 1988, when Algeria went through at the expense of Ivory Coast.
Quarter finals
Sat 31 January 2015
Congo vs Congo DR 16:00
Tunisia vs Equatorial Guinea19:30
Sun 1 Feb 2015
Ghana v Guinea 16:00
Ivory Coast v Algeria 19.30
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