The Indomitable Lions drew first blood after 72 minutes at Stade de Franceville through Michael Ngadeu-Ngadjui, before Christian Bassogog added the second deep into second-half stoppage time.
The result sets up an AFCON final clash against seven-time champions Egypt, with that tie to take place on Sunday at 21h00 SA time.
Speaking after their success over Ghana, Broos said: "It is a real dream for us to get to the final.
"Ghana have more experience than us - look at what they have done in recent tournaments. But since the start of this tournament, we have shown we keep going right to the end in every game.
"I am very happy, especially for the team. They are an exemplary group on and off the field and they deserve to be in the final."