The Ivorian notched a goal and an assist as Jose Mourinho's men put their London rivals to the sword in the first half, with substitute Loic Remy striking after the break
Spain forward Costa - scorer of 11 goals in 11 Premier League matches this season - missed Wednesday's London derby at Stamford Bridge due to suspension, but that mattered little.
|VIEW FROM STAMFORD BRIDGE
|By Greg Stobart
On this evidence Tottenham's unenviable record of failing to win away at Chelsea since 1990 is going to carry on for a good few years yet, given the gulf in class between the sides.
Spurs looked bright early on and hit the crossbar through Harry Kane, but they never win here and once Chelsea took the lead in the 19th minute they never looked back.
With star striker Diego Costa suspended, the burden fell on 36-year-old Didier Drogba to roll back the years and lead the line for the hosts - and he didn't disappoint.
The Ivorian set up Eden Hazard's opener with a lovely flick before scoring the second himself with a clinical finish.
Chelsea took their foot off the gas in the second-half and completed the scoreline when Loic Remy turned Jan Vertonghen inside out before coolly slotting into the top corner.
That makes it seven wins out of seven for Chelsea at home in the Premier League this season and on this evidence it's hard to see anyone beating them at Stamford Bridge this season.
Harry Kane hit the crossbar early on for Tottenham, but Chelsea responded like the champions many fancy them to become with two quick-fire goals.
Eden Hazard set Chelsea on their way in the 19th minute before Drogba netted less than 180 seconds later for his second league goal of the season.
Substitute Loic Remy, who replaced Drogba, sealed the convincing home win 17 minutes from time as Tottenham's winless run at Chelsea - which dates back to 1990 - continued.
Despite the absence of Costa, Chelsea fielded a familiar and settled line-up, while Tottenham, fresh from six wins in their last seven matches in all competitions, made just one change - with Roberto Soldado dropping to the bench despite his rare goal in a 2-1 win over Everton on Sunday.
Erik Lamela replaced Soldado for Spurs, who started brightly, and only the woodwork denied Kane in the seventh minute.
Aaron Lennon, continuing to impress after a recent recall, crossed for Kane from the right and the striker peeled off Gary Cahill to steer a header onto the bar, with goalkeeper Thibaut Courtois well beaten.
Kane then stripped Cahill off the ball in the 12th minute and charged into the box, only shooting just wide with his left foot.
The early chances buoyed the vocal travelling supporters, but they were soon silenced by a simple but brilliant Chelsea move.
Hazard played a neat one-two with Drogba and the Belgian glided past three Tottenham players before shooting under Lloris from a tight angle.
And Lloris was to blame for Chelsea's second goal - scored just three minutes later - after his sloppy clearance fell to Hazard.
He fed Oscar and the Brazilian's excellent ball played in Drogba, who beat Jan Vertonghen and took two touches before slotting home.
Chelsea dropped the tempo slightly following Drogba's strike, happy with their two-goal lead, but Willian shot twice at Lloris as the first half winded down.
Cahill took a knock to the head in the early stages, and was replaced at the break by highly rated Kurt Zouma, who had work to do early as Chelsea sat back.
The best Spurs could muster, though, was a tame Christian Eriksen shot from distance, and a wayward Vertonghen header, before Drogba came off to a healthy ovation.
And his replacement, Remy, wrapped up the three points, beating Vertonghen with strength before side-footing past Lloris in stylish fashion as Chelsea underlined exactly why they are considered title favourites with a dominant display.