Cole, who last scored against Wigan in May 2010, lifted an 85th-minute winner over visiting goalkeeper Asmir Begovic after the ball had been knocked into the box by Juan Mata.
Cole's winner was tough on Stoke who had defended doggedly and had chances themselves with Marc Wilson testing Petr Cech from long range and Jonathan Walters and Matthew Etherington both firing wide.
But Roberto Di Matteo's men also looked dangerous, Fernando Torres scuffing the best chance into the arms of Begovic in the first half, and Oscar twice being denied by the excellent Potters goalkeeper.
Southampton stormed back from behind to earn their first points of the season with an emphatic 4-1 triumph over ailing Aston Villa at St Mary's.
It looked like being the same old story for Saints, who had lost their first four matches back in the top flight, when Darren Bent pounced on hesitant defending to sweep home a 36th-minute opener.
Rickie Lambert lashed home the Saints' equaliser on 58 minutes and five minutes later they were ahead when defender Nathaniel Clyne slotted past Villa goalkeeper Brad Guzan.
Saints made sure of victory on 72 minutes when Jason Puncheon's right-footed drive took a heavy deflection off Ciaran Clark, and Lambert sealed victory with a penalty in the dying seconds.
Steven Fletcher scored his fourth goal in three appearances for Sunderland but it was not enough to claim three points for the Black Cats as West Ham snatched a late 1-1 draw at Upton Park.
Fletcher finished off a fine Sebastian Larsson cross in the ninth minute and came close to a second soon afterwards when his effort in the box was blocked by James Collins.
Sam Allardyce's men poured on the pressure with both Ricardo Vaz Te and Kevin Nolan coming close before Nolan volleyed the equaliser in injury time from a header down by substitute Modibo Maiga.
West Brom continued their superb start to the season as Romelu Lukaku drilled the only goal of the game in the 71st minute to see off Reading 1-0 at The Hawthorns.
Hugo Rodallega came back to haunt his former club as he netted the opener for Fulham in a 2-1 win against Wigan at the DW Stadium.
Rodallega's 31st-minute header set Fulham on their way to three points and Damien Duff slotted home to make it 2-0 on 68 minutes. Arouna Kone netted an injury-time consolation for the hosts.
In the early kick-off, Everton continued their promising start to the season by coasting to a 3-0 win at Swansea.
Victor Anichebe opened the scoring on 21 minutes and Kevin Mirallas and Marouane Fellaini added further goals, while the Swans were reduced to 10 men after substitute Nathan Dyer's 58th-minute dismissal.
Saturday's Barclays Premier League Results
Swansea 0-3 Everton
Chelsea 1-0 Stoke
Southampton 4-1 Aston Villa
West Ham 1-1 Sunderland
West Brom 1-0 Reading
Wigan 1-2 Fulham