After the game was suspended due to rains on Sunday, Sadick recovered from his troublesome thigh injury to score the all-important goal for Steve Polack's outfit late in rematch.
Kotoko had the better start to the game, tormenting Medeama’s back-four but were dealt a big blow by the 22nd minute when midfielder Seth Opare was forced to take early shower through an injury and was replaced by Evans Quao.
The substitution affected Kotoko as it sapped some strength from their game plan since Quao was a make-shift defensive midfielder. However, neither side could create a breach for the opener.
Medeama had a chance to open the scoring on 49th minute, with Kwesi Donsu breaking loose in a quick counterattack, but the midfielder's last pass to Latif Salifu for a simple tap in was blocked by Awal.
On the other side, Frank Sarfo Gyamfi was played through by Kwame Boahene but the midfielder's last ditch effort went agonisingly wide with only goalkeeper Yaw Ansah to beat. Yakubu Mohammed also missed some decent opportunities to add up to the supporters frustrations on the day.
On the 57th minute, Kotoko appealed for a penalty after Sarfo Gyamfi appeared to have been tripped in Medeama's box, but they were ignored by referee Awal Mohammed.
Kotoko brought on Sadick Adams for Yakubu on 65th minute and he nearly scored the opener with his first touch. A cross from Boahene came off Medeama's defender Paul Aidoo and Sadick couldn't control his first touch, giving goalkeeper Ansah time to recover and made a goal line clearance.
Sadick had two successive opportunities with 10 minutes left, after he was set up by Jackson Owusu but the former Atletico Madrid youth star remained wasteful.
However, Sadick made amends in extra-time after he connected Eric Donkor's pass for the opener on 106 minute. Although, Medeama players protested that he initially handled the ball, the referee stood on his ground.
Kotoko held on to make it to the final but were left off the hook with three minutes remaining when Edmund Peprah rounded goalkeeper Felix Annan but the striker's effort was denied by the goalpost.
Hearts of Oak, who also defeated Wa All Stars 2-1 on Sunday, will now lock horns with Kotoko in the final scheduled for October 29 at the Tamales Sports Stadium. This will be the first Super Clash in the FA Cup final since 1990 but it is Kotoko's fourth appearances in the final since 2011.