Jose Bosingwa signalled the Blues' early intent when on eight minutes he rattled Carlo Cudicini's crossbar with a 20-yard piledriver.
Spurs countered with two fine efforts on 11 and 13 minutes - Jermain Defoe and Tom Huddlestone both foiled by Chelsea keeper Petr Cech.
Cech was beaten a minute later but Jermaine Jenas's long-range shot was inches wide of the Chelsea goal.
On 31 minutes Michael Ballack went flying in the box from a challenge by Vedran Corluka but referee Howard Webb ignored the penalty appeals.
But seconds later and Stamford Bridge erupted as Cole scored. The left-back met a deep right-wing cross by Drogba with a diving header from six yards which sailed past a helpless Cudicini
Frank Lampard could have sealed the points two minutes into the second half but his side-footer from a Drogba pass was well wide.
Ledley King limped off seconds later and was replaced by Alan Hutton on 48 minutes to add to Spurs' woes
Robbie Keane claimed a penalty on 56 minute when Bosingwa challenged him on the Chelsea byline but again Webb waved play on, much to the Irishman's fury.
Within a minute Chelsea doubled their lead. Nicolas Anelka crossed from the right and the ball fell to Drogba, whose low left-footer was parried by Cudicini.
Lampard scooped up the ball from the post and cut it back to Ballack, who tucked it home from five yards.
The points were wrapped up on 63 minutes when Cole set Drogba away and he out-paced Corluka.
The Croatian then put in a challenge which deflected the ball past Cudicini and Drogba followed up by slamming the ball into the empty net.
Benoit Assou-Ekotto then handled from a Lampard free-kick in the penalty area but got away with it.
Crouch was brought on in the 67th minute and within seconds out-jumped John Terry to knock the ball down for Wilson Palacios, who screwed his half-volley just wide of Cech's right post.
The beanpole striker than had a run and shot all by himself but he arrowed over the Chelsea goal with 20 minutes remaining.
A 10-minute delay resulted from an injury to Sebastien Bassong and Drogba followed suit within the minute after pulling up with an apparent calf injury which could keep him out for several weeks.
Spurs' bright start to the season is over while Chelsea's seventh win a row - six in the league - leaves then clear at the top and three points ahead of Manchester United.