A brace from Blues winger Hakim Ziyech gave last season's Champions League winners a lead their performance to that point deserved before Lucas Moura and Steven Bergwijn struck twice in 14 second-half minutes to wipe out their advantage.
Fresh from Sunday's win over Arsenal in the opening game of "The Mind Series" -- a preseason competition between the Blues, Spurs and the Gunners organised to support better mental health -- Thomas Tuchel's side started strongly before approximately 25,000 fans at Stamford Bridge.
Ziyech drove home his first from 20 yards after 16 minutes before netting again just three minutes into the second period. However, Spurs improved thereafter with Moura's heavily-deflected shot halving the deficit and Bergwijn's low finish restoring parity.
Tottenham were without Harry Kane after he failed to report back for preseason training as planned with the 28-year-old seeking a move to Manchester City but Son Heung-Min, who recently signed a new four-year deal, started in attack with Pierre-Emile Hojbjerg, Dele Alli, Eric Dier and Sergio Reguilon among those also included in the line-up.
Kante had excelled in the Champions League Final win against Manchester City -- Cesar Azpilicueta brought the trophy out to a guard of honour and rapturous applause before kickoff -- and he picked up that form in west London, helping the home side take firm control after Son's fifth-minute low drive forced Edouard Mendy into an early save.
Spurs quickly looked overrun in midfield and as Moura picked up the ball and looked to drive over the halfway line, he was stopped in his tracks by a superb trademark tackle from Kante.
The loose ball fell to Ziyech and he took advantage of the space ahead of him to drive forward into a central position before unleashing a left-foot drive past new Spurs goalkeeper Pierluigi Gollini, who joined the club in July on an initial season-long loan from Atalanta.
Chelsea continued to dominate and Timo Werner rounded Gollini to score just before the interval but his goal was ruled out -- incorrectly -- for offside.
Spurs boss Nuno Espirito Santo introduced Harry Winks for Hojbjerg at the interval as Chelsea brought on Pulisic and Tiemoue Bakayoko for Kante and Callum Hudson-Odoi but the Blues initially continued in the ascendancy.
Four minutes into the second half Werner, Kai Havertz and Alonso combined to find Ziyech in the box and his shot took a nick off Eric Dier before finding the net.
Spurs began their revival just before the hour mark when Moura's shot deflected heavily off Antonio Rudiger and looped into the net.
Tuchel then made seven changes -- including academy graduate Dijon Sterling, who tested Collina moments after coming on with a low left-foot shot from the edge of the box -- but the Blues inevitably looked more disjointed as mistakes began to creep in.
And Spurs capitalised with 20 minutes remaining when another substitute -- Malang Sarr -- lost the ball allowing the visitors to break, Son feeding Bergwijn to finish low through Mendy's legs.
Ben Davies, another second-half introduction, almost won it with a left-foot shot which Ethan Ampadu cleared off the line but the spoils were shared in a match from which both sides will take positives as they build up to competitive action next week with Chelsea set to face Villarreal in the UEFA Super Cup Final on Aug. 11.
Spurs play Arsenal in their final preseason friendly on Sunday.