After beating West Brom in the Carling Cup, the League One side scored two second-half goals to chalk up the first round-three upset after their 1pm kick-off.
And they fully deserved their success after a positive display that unsettled the Potters from start to finish.
Stoke were hit by injuries and suspension before the game and Hartlepool had problems of their own once it started, losing right-back Antony Sweeney on 17 minutes and striker Michael Mackay on 32, both of them to injuries.
But there had been problems for them early on with Rory Delap taking his first long throw as early as the opening minute.
That was cleared, as was a corner seconds later after Ibrahima Sonko's effort at the near post hit the woodwork before being scrambled away.
But it wasn't one-way traffic and on nine minutes Andrew Davies headed off the Stoke line after a Matty Robson corner caused problem for the Potters defence.
Just before half-time, City keeper Steve Simonsen did well to hold a Robson cross that was deflected in the area.
Three minutes after the break, Hartlepool jumped in front as defender Michael Nelson headed Robson's left-wing free-kick in at the far post.
And as Stoke's attempt to come back showed signs of petering out, Hartlepool made it 2-0 on 76 minutes with a brilliant goal from sub David Foley.
He was allowed to make a few yards of space before looping his 30-yard shot over Simonsen and into the top corner.
A minute later Delap, one of the few Stoke players to do well, broke into the home area on the left but placed his shot inches wide of the far post.