In the end a first-half goal from Florent Malouda and a second-half penalty from Drogba was the difference between the teams.
Even so Stoke could have made the champions pay for not taking their chances, notably when Glenn Whelan unleashed a thunderous 25-yard shot which ricocheted down from the underside of Petr Cech's crossbar and bounced to safety.
Chelsea, however, maintained their perfect start to the Premier League season and Ancelotti's side have now scored 14 goals and conceded none while Stoke are still searching for their first point of the season.
Ancelotti said: "I was happy because we won but we didn't have a good, high tempo. It was not our best performance.
"The tempo was not continuous but we didn't concede. We kept another clean sheet and stayed top of the table.
"We worked very hard this week. The players had a very strong week and so they were not so sharp."
Stoke manager Tony Pulis was pleased with his team's work-rate but accepted his side had been second best.
He said: "We had our moments but overall Chelsea were the better team.
"They have some great players and had numerous opportunities but I give credit to our lads for the work they put in."
Source: Team Talk
Source: Team Talk