Goalkeeper Hugo Lloris allowed a Pedro strike to sneak between his legs just short of the hour, before a miscommunication between the France international and Kieran Trippier saw the full-back roll a backpass into an open net.
Coming on the back of Saturday's 2-1 defeat to Burnley, the loss leaves Spurs eight points adrift of second-place Manchester City and nine off leaders Liverpool.
For Chelsea, who dropped Kepa Arrizabalaga in favour of Willy Caballero following the former's refusal to be subbed during the EFL Cup final, the result is the perfect response to their Wembley defeat against City on Sunday.
Chelsea had an opportunity to take an early lead when the ball fell to Gonzalo Higuain in the box after six minutes, but the on-loan Juventus striker did not hit the ball cleanly, finding only the right-hand post.
Ben Davies survived appeals for a penalty after a Cesar Azpilicueta cross struck his arm in the 12th minute, before a dreadful pass led to a Higuain effort that drifted wide.
Two minutes before the break, Harry Winks pulled the trigger from 25 yards with a shot that appeared to be dipping under Caballero's crossbar but bounced back off the woodwork.
The opener arrived 12 minutes into the second period, when Pedro collected the ball from Azpilicueta and drifted in from the right before spotting a gap to prod the ball past Lloris.
Spurs failed to register a single shot on target - at the right end, at least.
With six minutes to play, Trippier sealed Spurs' fate with a horribly misjudged backpass that rolled into the visitors' net with Lloris nowhere.
The perfect tonic for Blues
The baggage that came with Chelsea's EFL Cup final loss was almost as morale-sapping as the defeat itself, so victory in a London derby should raise spirits at Stamford Bridge.
Another reverse for Spurs and the nature in which it came may just signal the end of their challenge this season.
Pedro steals the limelight
While Caballero's serene display amid the furore surrounding his selection ensured he would avoid the back pages on Thursday, Pedro stepped up with an all-action showing in the second half.
Shortly after firing his side in front, the former Barcelona winger was back in his own box, dispossessing Christian Eriksen with a perfectly timed challenge.
