Playing with a man down following the sending off of Khaled Adenon, The Squirrels held their own for a 1-1 draw after regulation time before coming tops in a penalty shootout (4-1).
It could all have all ended in stoppage time for Benin when the Atlas Lions were awarded a penalty but Hakim Ziyech's missed effort gave the west Africans a lifeline.
"I am very proud of my team," Dussuyer said at the post-match presser.
"We had a difficult game.
"Morocco are a very strong team but we mentally prepared ourselves well and luck was on our side tonight.
"Playing with one man less was difficult and we will try to make amends for Khaled Adenon, who will miss the next match [against Senegal].
"I thank my boys for the remarkable efforts made tonight, I think we can continue this beautiful dream."
It is indeed an incredible run for Benin who only sneaked into the knockout stage as one of the four best third-placed sides after drawing all three group games. It is their first time of making this stage of the championship.
Interestingly, The Squirrels, who are making their fourth tournament appearance at Afcon, are still chasing their first win after 13 matches.