Coventry, who posted a narrow 1-0 victory in the Potteries when the two sides met here in their league fixture back in November, struggled to carve out a notable first-half chance, besides recent loan acquisition Yang Min-hyeok curling an effort wide.
The Potters continued to appear the more threatening and ought to have taken the lead before half-time when Mubama, from inside the six-yard box and with the goal at his mercy, could only turn the ball over the crossbar.
Coventry’s performance levels markedly improved at the beginning of the second half, although they needed Wilson to be on his toes to beat away Rigo’s stinging drive at the other end, moments before Ben Wilmot nodded just wide of the far post.
Romain Esse, another transfer window addition, lifted the visiting fans behind the goal off their seats when he skilfully beat Maksym Talovierov and teed up Wright at the back post, but the American crashed his header against the woodwork.
The Sky Blues went close again to breaking the deadlock when Rudoni’s attempt from the edge of the penalty area clipped the leg of defender Ashley Phillips and struck the post.
But Stoke made their visitors pay for failing to take advantage of their growing dominance and sealed progress just as extra time loomed – Cisse, fouled in the build-up, re-joined the attack and planted his strike beyond the dive of Wilson to win it.