Following a 1-1 draw after regulations time, the game was forced into penalties where the visiting Porcupines proved superior at the Accra Sports Stadium.
Kotoko will face Karela United in the final of the championship following the latter's 1-0 away triumph over Ashanti Gold in the other semifinal tie on Sunday.
It was Kotoko who netted first in the game as early as the fourth minute when Abdul Safiu Fatawu, who just rejoined the Porcupines from international duty ahead of the game after failing to make Ghana's final 23-man squad for the upcoming Africa Cup of Nations (Afcon) in Egypt, hit a low shot into the net following a Naby Laye Keita back heeled pass.
Kotoko held on to their slim lead until the third minute of injury time when Hearts drew level through a Christopher Bonney penalty.
Without any further late goal, the match was forced into a straight shootout which would eventually be won by the Porcupines.
Kofi Kordzi, Christopher Bonney, Robert Addo and Abubakar Traore converted Hearts' first four kicks before centre-back Mohammed Alhassan, who like Fatawu, had been away on international duty with the Black Stars, missed the Phobians' final effort.
Kotoko's fifth penalty taker Amos Frimpong, on the other hand, made no mistake to make it five successful kicks following earlier strikes by Ismail Abdul Ganiyu, Jordan Opoku, Evans Owusu and Fatawu.
On June 23, Kotoko will face Karela United in the final as the Anyinase-based outfit recorded a stunning 1-0 away victory over Ashanti Gold in the second semifinal tie.
Diawisie Taylor's strike made the difference in Obuasi.
The ultimate winners of the competition will represent Ghana in next season's Caf Champions League.