The win sees Tottenham leapfrog Chelsea into third place, two points proving the difference.
Spurs quick out the blocks
Harry Kane tested the new Chelsea goalkeeper just a matter of minutes into the game but his header was caught easily by Kepa Arrizabalaga.
Spurs' continued pressure paid off as Dele Alli put the hosts ahead.
Christian Eriksen's free-kick was nodded goal bound by Alli which proved too hot for the Chelsea keeper to handle.
Alli continuing from where he left off with Chelsea after scoring a brace in the 2-1 win against the Blues at Stamford Bridge last season.
Chelsea did have an appeal for a penalty kick after it seemed Juan Foyth took down Eden Hazard but Martin Atkinson was not interested.
Just minutes later, Spurs should have had their lead doubled.
Heung-min Son teamed up with Eriksen but was unable to convert the half-volleyed attempt which soared over the bar.
Harry Kane doubled Tottenham's lead after just 15-minutes from distance.
The England captain had all the time in the world to turn and get his shot away from around 25 yards which wrong-footed the young keeper.
It was almost a third for Spurs but Toby Alderweireld's close ranged effort was expertly saved by Kepa and Foyth could not convert the rebound.
Hazard tried his luck from 20-yards out with very few options ahead of him but Hugo Lloris was equal to the driven effort.
Just before the interval, Eriksen provided Son with a stunning cross but once again the South Korean was unable to convert with Kepa pulling off another sublime save.
Despite being denied what seemed a debatable penalty, Chelsea will have been thankful the deficit was only two goals as the referee blew for half-time.
Spurs continue to impress
Although the Blues started brighter in the second half, Son stretched their lead to three.
Superb dribbling from the edge of the Chelsea half, down the wing and then into the box before slotting the ball beyond Kepa.
Son should arguably have been making this his hat-trick but the Spurs fans wouldn't mind with Spurs comfortably ahead.
Now with a secure lead, Spurs continued to toy with Chelsea and really should have converted another couple of opportunities.
With their chances of a revival shortening, Chelsea fans will have thought their day couldn't have got any worse when Hazard stayed down after a heavy challenge from Serge Aurier.
However, slowly the Belgian returned to his feet.
With just five minutes remaining, the visitors pulled one back through Olivier Giroud.
A perfectly weighted cross from Marcos Alonso found the substitute unmarked in the box and the Frenchman got the better of his country's captain.
But it was all too little too late for Chelsea in what was an embarrassing performance from the visitors.