Nwakaeme scored in the 43rd minute to put Trabzonspor 3-0 ahead.
It was his second goal in the competition after also scoring in the 2-0 win against Denizlispor on January 16.
Former Super Eagles captain John Mikel Obi did not feature in the game as he was an unused substitute.
The second-leg comes up on February 13 with the winner progressing into the semi-final.
The last time Trabzonspor won the Turkish Cup was in the 2009/2010 season when they beat Fenerbahce 3-1 in the final.