Chelsea maintains perfect record
Roman Abramovich looked on as the Blues unleashed the £80m trio of Eden Hazard, Oscar and Juan Mata for the first time behind £50m man Fernando Torres.
But the quartet were nowhere near being the 'Barcelona in blue shirts' the club's billionaire owner craves until the 85th minute, when Cole finished a brilliant move to snatch a barely-deserved win.
It could easily have been a fourth straight match without a victory for Chelsea as Torres flopped once again and Jonathan Walters hit the crossbar for Stoke, who arguably had the better of the chances.
That would have cranked up the pressure on Blues boss Roberto Di Matteo, who shrugged off Thursday's visit of Abramovich to the club's training ground the morning after the club's opening Champions League game against Juventus.
After his gamble at picking Oscar in that 2-2 draw paid off spectacularly, Di Matteo was emboldened enough to leave out both John Terry and Frank Lampard.
But despite Chelsea enjoying more of the ball, Torres, Hazard, Oscar and Mata played like the strangers they were for most of the afternoon.
Torres did nod a Mata corner over the top but, otherwise, the Champions League winners were guilty of taking too many touches, making one pass too many and allowing Stoke to smother.
The visitors should have made them pay in the 20th minute when an unmarked Walters thumped a header from Glenn Whelan's free-kick against the crossbar.
Branislav Ivanovic was lucky to avoid a yellow card for a shameful dive in the box but no referee could have failed to book Charlie Adam for rugby-tackling Ramires.
Torres is rarely upstaged when it comes to embarrassing moments and he duly added another to his collection with an air-shot after Mata's wonderful dink put him one-on-one with Asmir Begovic.
At the other end, Michael Kightly almost redirected Geoff Cameron's fizzing cross past Petr Cech, while Chelsea's half was summed up when David Luiz smashed a wild shot high into the Shed End.
The home side were not exactly booed off at the break but a flat atmosphere certainly greeted them after the restart.
That changed when Chelsea were denied the latest in a cataloge of recent penalty claims when Oscar went down under Ryan Shawcross' challenge.
It may not have been a spot-kick but did not deserve the acting award that followed - a booking.
That sparked Chelsea and Oscar to life and the Brazilian tested Begovic with a low shot before Mata blazed wide following a defensive mix-up.
Stoke settled and Peter Crouch, Walters and Adam all had sighters before Di Matteo withdrew Hazard for Victor Moses just past the hour mark.
The Potters responded by sending on Michael Owen for Adam but Chelsea almost cut them open when Mata was thwarted by a brilliant Shawcross tackle.
Oscar was becoming more and more of a threat and his deflected grass-cutter was well saved by Begovic before he sent another mid-range shot narrowly wide.
Matthew Etherington replaced Kightly and Cameron Jerome came on for Crouch as Stoke sensed more than a draw.
Etherington dragged wide after John Obi Mikel, of all people, should have done better than squander what was a fine pass by Torres.
Mikel departed for Lampard for the final nine minutes and, four minutes later, Chelsea finally had the breakthrough.
It was the first piece of Barcelona-esque football of the entire afternoon as some lovely build-up ended when Mata's delightful back-heel found Cole, who lifted the ball beyond Begovic.
A brilliant last-ditch Etherington tackle prevented Moses having a chance to make it 2-0 on the break. Terry came on for Mata and a late Luiz tackle on Walters ensured the game ended with some bad blood between the sides, with Etherington also involved in a minor altercation with Ivanovic before the final whistle.