Alli then made his mark after the break with two goals in quick succession, first breaking the offside trap to finish Eric Dier's long ball after 62 minutes before tapping home a scruffy move four minutes later to claim an historic win for Spurs.
The victory boosts Spurs' hopes of beating Liverpool to a top-three finish, while Antonio Conte's Blues must now close an eight-point gap on their London rivals if they are to qualify for next season's Champions League.
Mauricio Pochettino's men had the majority of possession in the first half, but struggled to find a way through Chelsea's solid three-man defence with Heung-min Son isolated in a lone forward role as Harry Kane - back from his ankle injury - watched on from the bench.
Chelsea looked dangerous on the break as Willian drew a decent stop from Lloris, and had a goal disallowed 20 minutes in after Marcos Alonso's low volley was ruled out for offside.
The hosts did make the breakthrough nine minutes later, and it came after an error from Lloris.
Victor Moses hung up a high cross into the Spurs penalty area, and France's No.1 goalkeeper was left grasping at thin air as he missed the ball to allow Morata the simple task of heading into the corner of an empty net.
Lloris went some way to atoning for his earlier error with a strong low saw to deny Alonso two minutes from the interval, and Davinson Sanchez made a fine block from an N'Golo Kante drive soon after - but it was Spurs who made their mark before half-time.
Alli did well to keep the ball in play deep in Chelsea's half, and with Moses failing to clear his lines, Eriksen unleashed a vicious, dipping 25-yard effort which flew over the top of a helpless Caballero to level things up heading into the second half.
Chelsea were listless after the break, and were slow to react to Dier's long ball over the top of their defence as Alli took a great first touch before dinking the ball past Caballero to put Spurs in front after 62 minutes.
If that goal was meant to spark Chelsea into life, the hosts failed to get the message as Alli had his second of the game four minutes later as the England youngster reacted fastest following a loose ball after Son saw two efforts blocked.
Conte furiously kicked nearby water bottles on the touchline in frustration, while Pochettino even had to luxury of bringing Kane off the bench for his first-team return as Spurs frustrated the home crowd to see out the result.
Chelsea have now lost an proud 18-year unbeaten home record to Spurs, and Conte's future looks increasingly uncertain as the FA Cup remains the Blues' last remaining ray of hope in a desperately disappointing second season in English football for the Italian coach. THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>