An Amos Frimpong penalty and a Maxwell Baakoh effort sealed the victory for the Porcupine Warriors at Baba Yara Stadium in Kumasi, the visitors' consolation coming from Oumarou Sali.
Charles 'CK' Akonnor's charges progress to the 'money zone' on a 5-3 aggregate, having won the first leg 3-2 in Yaounde.
The draw for the group stage is slated for Monday.
Akonnor made one change to the side that started the first leg as Abass Mohammed came in at left-back, pushing out Augustine Sefa.
Bertin Ebwelle of Coton Sport, on the other hand, brought five new faces into his XI. Banga Bindjeme, Kalamou Moussa, Oumarou Sali, Marou Souaibou and Mangolo Aime took the places of Thomas Etta, Ngweni Ndassi, Youssoufa Malkano, Maximilien Elimbi, and Marcel Batai.
With a huge crowd behind them, Kotoko started brightly, taking the game to Coton Sport as Emmanuel Gyamfi forced goalkeeper Bassa Djeri to spill a shot in the first minute.
The visitors came more and more into the game as it travelled. Clear-cut chances, though, were hard to come by for either side.
When it looked headed for a barren first period, the Porcupine Warriors broke the deadlock on the stroke of half-time through captain Amos Frimpong, who stepped up to convert a penalty after Songne Yacouba was fouled in the box.
Shortly after the interval, Kotoko went 2-0 up as Baakoh got on the end of a drop-ball and shot into the far corner beyond Djeri.
Coton Sport, however, would not give up. After a few goal attempts, the Cameroonians eventually pulled a goal back through Sali, who capitalised on a loose marking inside the box to plant the ball at the back of the net.
Apparently energised by their consolation, Les Cotonniers poured forth for the equaliser but the home side firmly held on to the score to book a ticket for the next round.