Eden Hazard was the only man in the shootout who failed to convert his spot-kick, the playmaker stepping up last and seeing his effort saved by Jack Butland to increase Blues boss Mourinho's woes.
The visitors had suffered an early setback in the fourth-round clash when Diego Costa was forced off injured in the first half, and they subsequently fell behind when Jonathan Walters cracked a superb 52nd-minute effort in off the bar.
The visitors snatched a leveller in stoppage time through substitute Loic Remy, moments before Phil Bardsley's sending off gave them a man advantage, but were ultimately unable to make the most of it as they succumbed to their latest defeat.
Chelsea went into the tie with the sense of crisis around them having increased after Saturday's trip to West Ham ended in another damaging Premier League defeat and saw Mourinho - subsequently hit once again by a misconduct charge from the Football Association - sent to the stands.
Talk has been rife of the Portuguese being on the brink of losing his job, and it will certainly be interesting to see what the future holds for him now after he failed to find any comfort in a cup competition he has won three times, including last season.
Mourinho named a strong starting XI featuring only three changes from the West Ham game, and his men made a lively start.
Butland did well to keep out a fifth-minute Costa shot, who then delivered a deflected cross which was kept out on the line by Glenn Whelan
Oscar saw one effort palmed over by Butland and another curl across the face of goal, before Costa won a free-kick as he was sandwiched between Ryan Shawcross and Charlie Adam.
Not long after, the Spain striker, having just tried to muscle his way in as Butland punched away a Willian cross, was down on the turf while Marc Muniesa acrobatically fired on to the roof of the net at the other end.
And moments later - the visitors having threatened again via Ramires' shot into the side-netting - Costa headed off and down the tunnel clutching his side, Remy replacing him.
Adam subsequently brought a save out of Asmir Begovic, before Eden Hazard's shot was batted behind by Butland.
Begovic then made a great reaction save with his legs in first-half stoppage time to keep out a Walters strike.
The Potters forward would not be denied for long
Shortly after the interval - and the departure from the field of the injured Muniesa - Whelan teed up Walters, who had the space to turn and send a fantastic strike bouncing in off the underside of bar.
Kurt Zouma and substitutes Robert Kenedy and Bertrand Traore were unable to convert equaliser attempts, and Walters also missed a couple of chances to add to his effort.
Stoppage time then saw things dramatically turn in Chelsea's favour, with Remy rifling in Zouma's knock-down from a Willian corner and Bardsley being shown a second yellow card after a tackle on Kenedy.
The first half of the additional period saw Chelsea threaten through Hazard and a Traore header, while Marko Arnautovic looped a shot just wide of Begovic's post.
Willian went close in the second 15 minutes and Butland saved from Traore with his feet before touching the ball away as it skidded goalwards off Kenedy.
The England goalkeeper then proved the hero of the night - with Hazard the villain - as he made the decisive intervention in the shootout to send Stoke through to the quarter-finals.
Source : PA