Following a 1-1 draw after normal time, the match headed straight into penalties, where the Porcupines emerged 4-1 victors at home at the Baba Yara Sports Stadium in Kumasi.
It was Karela who netted first on the day through Osei Baffour, whose curling shot from inside the box beat goalkeeper Osei Kwame.
Kotoko had to wait until the 71st minute to level the score when Abdul Safiu Fatawu converted a penalty after the attacker was tripped in the penalty box.
Without any further goals, the game moved straight into penalties after 90 minutes without extra time, as per the competition's regulations.
In the shootout, Karela missed their first two kicks as Patrick Yeboah and Ampem Dacosta could not find a way past goalkeeper Osei.
And although Agyemang Yeboah subsequently converted for the away side, Ismail Abdul Ganiyu, Daniel Darkwah, Fatawu and Naby Laye Keita slotted in all four of Kotoko's kicks to seal a 4-1 win.
Next season, the Porcupines will hope to better this term's performance in Africa, where they reached the group stage of the Confederation Cup.
In the absence of the Ghana Premier League, which is set to return next season, the Special Competition was organised to "keep clubs busy" and to select a representative for the Champions League.