The Potters looked to have held on for a deserved point until the 85th minute, when Cole coolly finished from close range to notch his first top-flight strike for two years and keep the Blues on top of the pile.
Brazil starlet Oscar made his first Premier League start for the Blues after his stunning goal-scoring debut in the Champions League in midweek, while Petr Cech took the captain's armband as John Terry and Frank Lampard were consigned to the substitutes bench.
Former Chelsea defender Robert Huth lined up for the visitors as they went in search of their first win of the season, having drawn their opening four league matches before their ignominious defeat to Swindon in the Capital One Cup.
The hosts began to dictate play from the off, with Stoke seemingly content to get as many men behind the ball as possible while allowing the likes of Juan Mata, Eden Hazard and Oscar to keep possession so long as they didn’t encroach on the penalty area.
Despite their early monopoly of the ball, Chelsea were struggling to find a way to break down Tony Pulis' side and were fortunate not go a goal behind on the 20-minute mark. Glen Whelan whipped in a dangerous delivery from a free-kick to the right-hand side, John Walters ghosted in completely unmarked at the near post and flicked a header goalwards only to see the ball clip the top of the crossbar, with Cech motionless in the middle of his goal.
Chelsea responded with some sustained pressure and Branislav Ivanovic had a shout for a penalty waved away after he turned past Huth in the box, with replays showing he went to ground a little too readily for referee Michael Oliver's liking although there was some contact between the players.
The Blues continued to dictate without finding a way through to Asmir Begovic's goal, until Fernando Torres missed the best chance of the half for the hosts. Juan Mata clipped a simple ball over the top of the back four from the edge of the area, but the Spain striker couldn't quite bring it down on his chest and Begovic was off his line smartly to smother the danger.
Stoke's resilience was beginning to frustrate Roberto Di Matteo's side. David Luiz tried his luck with an ambitious free-kick and Hazard scuffed a cross-come-shot wide of the far post, which only added to the tension around Stamford Bridge.
Indeed, the hosts had Cech to thank for preventing their frustration from growing as the Czech keeper was twice called into action as the half drew to a close. First he denied Marc Wilson from long-range as Chelsea failed to close him down, before diving smartly to save from Michael Kightly's header after good interplay between Peter Crouch and Geoff Cameron.
Chelsea started the second half brightly and were denied another appeal for a penalty when Oscar burst through the middle before going down under a challenge from Huth. There was definite contact between the two although it was outside of the box, but referee Oliver opted to show a harsh yellow to the Brazilian for diving.
The Blues continued to hammer at the Potters' door, with first Oscar and then Torres being denied by the exploits of Begovic, before Crouch attempted a spectacular volley at the other end which sailed over the bar as Stoke tried to regain a foothold in the match.
Mata thought he had finally found a way through after some brilliant interplay between Oscar and Moses, but a terrific last-ditch tackle from Ryan Shawcross denied him at the near post. Then, just a moment later, Oscar cut inside from the byline and hit a low drive which Begovic just managed to cling on to with Mata waiting to pounce.
Both sides continued to look lively going forward going into the final period of the game. First John Obi Mikel wasted a great chance as he dragged his shot wide of Begovic's left-hand post following Torres' pass, before substitutes Michael Owen and Kenwyne Jones combined to tee up Matthew Etherington inside the area, who likewise fluffed his lines.
It was a miss which Etherington and Stoke would ultimately rue, as Chelsea finally broke the deadlock with just five minutes remaining. Ashley Cole burst forward with the ball from the edge of his own area and continued into the box after laying off to substitute Frank Lampard. He found Hazard, whose cross was flicked on by Mata and Cole was left to dink the ball over Begovic from just six yards out to the relief of the home fans inside the Bridge.
Stoke tried to rally in the closing minutes but Chelsea held on for all three points, keeping them top of the Premier League pile and putting pressure on the Manchester clubs ahead of their huge respective clashes against Liverpool and Arsenal tomorrow.