They will meet Arsenal in Saturday's final after the Londoners thrashed a Singapore Select XI 4-0.
Roberto Martinez's Everton appeared the fitter of the two sides in an absorbing match that became more open as the teams tired.
Record signing Romelu Lukaku was a constant menace to the Stoke backline but the Belgian was guilty of wasting a number of chances, the worst coming in the 90th minute when he scuffed wide of Jakob Haugaard's goal after wriggling free of his markers.
Despite playing in sweltering temperatures at the Singapore National Stadium, both sides appeared committed to turning the contest into a thorough workout but were probably delighted to go straight to penalties after 90 minutes.
Everton were wasteful during the match but they were ruthless in the shootout, sending Haugaard the wrong way on every penalty before impressive skipper Jagielka sealed the contest 5-4 when he thumped his spotkick into the top right-hand corner.
"It was more than a pre-season game, we had to deal with the heat, humidity and difficult conditions but I felt on top of that it was very competitive, both sides pushed each other and winning the shootout was a great feeling," Martinez told reporters.
"All in all it was a terrific exercise and we can now look forward to participate in Saturday's final and play for the trophy."
Dutch midfielder Marco van Ginkel, on loan from Chelsea as part of the deal that took goalkeeper Asmir Begovic the other way, was the only man to miss from the spot when he blasted straight at Tim Howard on Stoke's second penalty.
Despite the defeat, Stoke manager Mark Hughes was content with his side's performance in a game when injury and fitness concerns prevented him from playing his strongest team.
"I thought it was a very accomplished performance, a good workout. I thought the guys acquitted themselves really well, individually and collectively. We looked strong, the timing of our runs was good and it was a good competitive game," he said.
Stoke will play the Singapore Select XI in Saturday's consolation game at the biennial pre-season tournament in Asia being hosted by the city-state for the first time.
(Editing by Justin Palmer)
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