Gyan, who also scored the only goal in the quarter-final win over hosts Angola, headed home in the 21st minute.
Nigeria enjoyed long periods of possession and created the best chances but Ghana held firm.
The Black Stars, who last won the continental tournament in 1982, will meet either holders Egypt or Algeria in Sunday's final at Luanda's November 11 stadium.
"I told my players we were going to play to reach the final and not to produce beautiful football, only the result matters, it's all about the result," Ghana coach Milovan Rajevac told a news conference.
"Nigeria had a few good chances. Our team is very young and we let them be dangerous because of this lack of experience," he added. "Defence is a very important thing in modern football."
"I would not say we lost against a better side. We lost to a youthful and enterprising side. We had possibilities to win this match but this is football."
Gyan almost doubled the lead three minutes later with a lob that went just over Vincent Enyeama's bar.
Nigeria piled on the pressure after the break and Martins went close again at the hour when his attempt to lift the ball past Kingson bounced off the Ghana keeper's chest.
The move almost paid off immediately when a forceful cross from Elderson Echiejile took a deflection off Yakubu's knee and went just wide.
