United went into their final Checkatrade Trophy Group A fixture knowing they had to win to secure progression to the knockout stages of the competition.
A cross from Nadesan early in the game had Sowerby interested but it was just too high and it drifted over his head and behind to safety.
The Potters responded with a good move of their own which saw Clucas cross from wide. Tymon recovered it, and it was eventually fed to Shenton 20-yards out. His shot took a deflection, but he had a second bite of the cherry when the half clearance from the corner came his way. He kept it low but it was always heading wide and into the Warwick Road End.
Stoke passed the ball well as they gained a foothold in the game but they couldn't quite get it together in the final third, with deliveries going astray. A sweeping move saw Verlinden control a raking 40-yard pass before stepping inside to take a shot. Collin dived low and he was relieved to see it smash into the side netting.
Good work from Sowerby at the other end took him past his man before clipping the ball into the box. Hope got up to meet it and Gyollai had to scramble across to parry the downward header away.
Nadesan almost found himself clean through when Sowerby allowed a drilled pass to roll through his legs unhindered. The striker enjoyed a lovely first touch but Wara stuck out a leg to stop him in his tracks before he could complete the shot.
In an end-to-end encounter United survived a loud appeal for a penalty when Shenton took a looped ball over the top on his toe inside the 'D'. It appeared to hit Liddle on the hand as it crossed the line but the referee immediately waved play on.
The Blues took the lead with 23 minutes on the clock when Grainger spun his man to make space for Hope. He pushed away from his man and pulled the ball back to Sowerby, who was steaming into space. The midfielder dropped a shoulder to open up a clean path and he didn't disappoint as he left Gyollai with no chance with a thunderbolt of an attempt which found its way into the back of the net via the underside of the bar.
Carlisle almost doubled the lead moments later when a defensive mix-up left Gyollai in no man's land, and the back line at sixes and sevens as blue shirts converged from all angles. Hope went for the empty target, from distance, but it skewed high and well wide.
A 28-yard Grainger free kick hit the wall and bent behind as the Cumbrians started to dominate, and the corner was tempting until Wara made amends for his foul by heading it away.
Hope was even closer when he latched onto a flick from a huge kick forward just as it entered the 18-yard box. His volley was struck with venom but it was just an inch the wrong side of the post.
The hosts were made to pay for their misses when the lively Simranjit Thandi found space to weave his way towards the corner flag. A firm cross was met by an intelligent run from Tyrese Campbell and he left Collin with no chance as he crunched his close-range header into the roof of the net.
It was the visitors who nearly registered again when Verlinden dragged the ball away from Glendon before taking a step into space. He had a clean sight of goal and his whistling effort wasn't too far away as it swirled its way just over the bar.
United regrouped and Gyollai pulled off a superb save when Sowerby eased his way into the box. He was ready to celebrate until the stopper somehow got across to palm the ball onto the bar. Souttar gratefully completed the clearance.
The opening exchanges of the second half lacked the zip seen in the first 45 minutes with both sides wasteful and hesitant in the final third. Some good passing approach play was on show at both ends, but concentration at the back meant meaningful space was at a premium.
Midfielder Mike Jones tried to make things happen when he burst through just after the hour, but Gyollai watched his punt all the way as it settled comfortably in his hands. That lifted spirits and Yates used pace to turn defence into attack as he patrolled the right flank. His cross was met by Nadesan but Gyollai was once more in the right place at the right time.
Jarvis sent a 19-yard free kick over the bar from the angle of the box as the Potters also looked for inspiration, but it was the Blues who thought they'd unpicked the lock when a one-touch move culminated with a cut back for Nadesan to strike. He thought he'd done enough with a thumping volley but it hit the outside of the post and spun behind to safety.
Shots from distance from Stoke were twice blocked by Liddle as things started to open up, and it needed a point-blank save from Collin as a deep free kick found Souttar on the march. His close range downward header was stopped on the line by the in-form Cumbrian keeper as he threw his body at it.
A first time cross from Grainger was clipped away by Souttar before Nadesan could get a touch, as United tried to mount a late attack, and Jones was a whisker away when he let fly from distance. The crowd thought it had gone in until it smacked the advertising hoardings.
The game drifted into penalties with United knowing that they were out of the competition, and with the young Stoke side going through unbeaten in all three fixtures of their group campaign.
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Goals
Carlisle United - Sowerby (23)
Stoke City - Campbell (34)
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Penalties (taken at the Waterworks End)
Grainger - thundered into the bottom left corner - 1-0
Dunwoody - placed bottom left, saved by Collin - 1-0
Yates - bottom right hand corner, keeper wrong way - 2-0
Campbell - calmly chipped as Collin dived - 2-1
Jones - smashed onto the underside of the bar - 2-1
Thandi - sent Collin the wrong way - 2-2
Nadesan - found the back of the net via the bar - 3-2
Clucas - carbon copy of the Nadesan kick - 3-3
McCarron - great penalty from the youngster - 4-3
Jarvis - sent Collin the wrong way - 4-4
Miller - keeper goes the right way, palms it away - 4-4
Shenton - puts it into the net to win the bonus point - 4-5
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Teams
Carlisle United - Collin, Miller, Liddle, Gillesphey, Grainger, Yates, Glendon (Jones 51), Slater (Bennett 70), Sowerby, Hope (McCarron 83), Nadesan. Subs - Gray, Devitt, Campbell, Egan.
Stoke City - Gyollai, Tymon, Clucas, Campbell, Verlinden (Pemberton 59), Shenton, Souttar, Jarvis, Thandi, Dunwoody, Wara. Subs - Deczki, Niakate, Waddington, Kyeremateng, Forrester, Toure.
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Referee - Mr Martin Coy
Attendance - 882 (71 away fans)