Ashley Coleâ€™s first Premier League goal since May 2010 allowed Roberto Di Matteoâ€™s Blues to go three points clear at the top of the table with their fourth win from five outings.
Tony Pulis could feel fairly hard done by as his Potters nearly did enough to earn a draw but a late lapse allowed left-back Cole to nip in and slot home in the 85th minute.
With five minutes remaining, Cole broke a top flight scoring drought of more than two years when he was unmarked at the back to fire home Juan Mataâ€™s clever backheel which came from Branislav Ivanovicâ€™s low rightwing cross.
It was a cruel blow for the Stoke defence who had done so well to thwart the likes of Fernando Torres, Eden Hazard and Oscar but in the end they came up short with the deftness of Mata, who was back to his usual sharpness, and the cool finish of Cole proving the difference.
Stoke hadnâ€™t scored in their last four matches at Stamford Bridge and prior to the game were a chance of emulating the Leicester City side of 1976 who accumulated five draws in a row to start the season.
They came close to opening the scoring when Jon Walters had a free header from just over six yards out but he could not hit the target when he really should have.
The 26th minute saw Torres not far off when he was found by a deft chip from Mata but the strikerâ€™s second touch after his initial control with the chest was pounced on by Stoke keeper Asmir Begovic.
Michael Kightly almost gave Stoke an opening late in the first half when he got on the end of Geoff Cameronâ€™s fierce cross from the right but Blue gloveman Petr Cech was able to get in the way of his close range effort.
The second half did not supply many out-and-out scoring opportunities but Oscar did his best to life the home fans after his splendid display in the Champions League draw with Juventus on Wednesday night. The Brazilian was denied by Begovic in the 67th minute with a well-struck shot from range which did install some positivity in the Blues players.
Stoke had half-chances to win it with substitute Kenwyne Jonesseeing his header saved by Cech not long before Cole scored the solitary goal of the contest to allow Chelsea to go three points clear at the summit with the Potters falling to 13th despite their first defeat of the campaign.
Stamford Bridge, Londdon â€“ 41,112
Yellow cards: CHE - Oscar 50â€™, David Luiz 90+2â€™
STO - Charlie Adam 23â€™