Tottenham missed two good chances early on - Harry Kane hitting the bar then dragging a shot wide - and Chelsea went ahead when Eden Hazard finished sweetly following a one-two with Drogba.
The striker, who replaced the suspended Diego Costa, then netted with a low shot following a Hugo Lloris mistake.
Substitute Loic Remy completed the win with a smart finish from 12 yards.
There was plenty to admire about Chelsea, who once again turned on the style for 10 first-half minutes to blow away their second-best opponents.
Tottenham, who are still without a win at Stamford Bridge since 1990, could not deal with the sublime skill of Hazard, the power and physicality of Drogba and the rampaging runs down the right from full-back Branislav Ivanovic.
Perhaps more pertinently, though, Jose Mourinho's men did it all without leading scorer Costa and, in the second half, minus Gary Cahill who suffered a head injury during an early clash with Jan Vertonghen.
But it might have been so different if Tottenham had taken their early chances.
Vertonghen had already headed over the bar when Kane rattled the woodwork with a header from Aaron Lennon's right-wing cross.
Moments later, the forward picked up on Cahill's mistake, drove forward into the box but took one touch too many and flashed his angled shot across the face of goal.
Those misses proved costly when Chelsea stunned the visitors with a quick one-two which all but killed the game as a contest.
First, Hazard rifled a left-footed shot beyond Lloris after being played in by Drogba.
Then, three minutes later, Lloris directed a goal-kick straight to Hazard. He passed to Oscar, who in turn fed Drogba and the Ivorian striker hammered the ball past the French keeper.
Chelsea completely bossed the second half - Cesc Fabregas pulling the strings - and it was no surprise when Remy made it three by getting goal-side of Vertonghen, who had a night to forget, before cutting inside and placing a shot beyond Lloris.
Spurs registered only their second effort on target in injury time, but Thibaut Courtois was not to be denied a fourth consecutive clean sheet as he acrobatically saved Nacer Chadli's shot.
Chelsea manager Jose Mourinho: "We played against a very good team and they showed that during some periods in the game.
"They started better than us and should have scored before us, but after our first goal our team became more stable and confident and we controlled the game.
"I'm really happy with the points, performance and spirit of the players. It's too heavy a result, though, for Tottenham."
Tottenham manager Mauricio Pochettino: "We're very disappointed because we created some chances to score and after we conceded in Chelsea's first action, the game changed. After two or three minutes we made a mistake and they scored again.
"But I want to congratulate my players because they were brave in the second half. Today you could see that we have a very young squad who need games.
"It's not because of that we lost. Chelsea were just very clinical in front of goal."
(BBC)
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