Gareth Bale scored his tenth goal in his last eight games for Spurs to set the tone for a famous night at White Hart Lane, and Gylfi Sigurdsson added a second inside the opening 20 minutes.
Jan Vertonghen completed the scoring in the second half as Andre Villas-Boas' side remained completely dominant, and it will take a monumental effort from Inter to recover in the second leg next week.
Bale tormented the Inter defence in the Champions League in 2010 and it took him just six minutes to offer the Italians a reminder of his quality with an excellent header into the bottom corner to put Spurs in front after rising high above his defender to meet Sigurdsson's left-wing cross.
But the Welshman was left incredulous a few minutes later after collecting a yellow card for diving in the box which rules him out of the return leg, although replays showed it was a good decision not to penalise Walter Gargano.
Inter keeper Samir Handanovic was being kept busy in the opening stages as Spurs kept up the intensity and had to get down well to his left to keep out a Jermain Defoe strike, but he did not escape after making another save from the same player in the 18th minute as Sigurdsson pounced on the rebound to make it 2-0.
Tottenham continued to impress for the remainder of the first half but were given a scare just before the interval as Inter nearly grabbed an away goal with their first meaningful attack, but Ricardo Alvarez dragged a shot wide from the edge of the area.
Vertonghen spurned a good chance at the back post from Bale's free-kick at the start of the second period but made amends in the 53rd minute when he took advantage of poor marking to head in a third.
Spurs were rampant by this point and looked like adding to their lead every time they went forward against a demoralised defence, with Bale firing just the wrong side of the post after one of his trademark runs and another flowing move ending with a smart save from Handanovic to deny Defoe.
Aaron Lennon also forced Handanovic into action after a thrilling surge as the crowd relished every attack, although there was the odd warning sign at the other end and Brad Friedel saved well with his feet from Rodrigo Palacio.
Tottenham kept their focus until the final whistle to deny Inter a precious away goal and will now travel to Italy fully confident of finishing the job, even without the suspended Bale.