Gareth Bale, Gylfi Sigurdsson and Jan Vertonghen were on target and it could have been more but for a string of fine saves from goalkeeper Samir Handanovic.
It was the ideal scenario - especially not conceding a goal, and Brad Friedel made a key save in the second half - but the lads will know it's far from over when they travel the San Siro on Thursday week, March 14.
Andre Villas-Boas made three changes to the team that started against Arsenal on Sunday.
Friedel was back in goal for Hugo Lloris, William Gallas returned in central defence for Michael Dawson and Jermain Defoe started up front with Emmanuel Adebayor out through injury.
The first half couldn't have started any better.
We looked lively from the off as Aaron Lennon's cross fell just behind Bale and Sigurdsson inside two minutes and we were soon ahead.
Sigurdsson did well down the left and whipped in a cross that Bale rose majestically to glance into the corner.
Bale soon turned provider for Defoe, who feinted to shoot on his right to create the space to lash in a shot with his left foot that Handanovic did well to turn away. Bale was next in line, his 25-yarder easier for the goalkeeper.
Matteo Kovacic had Inter's first effort of note, a rising effort from 20 yards but within seconds it was 2-0. This goal started at the feet of Mousa Dembele, who lost two players on the inside right channel before releasing Lennon down the right. His cross found Defoe, whose shot was parried by Handanovic into the path of Sigurdsson, who made no mistake from close range.
The chances kept coming - Vertonghen looped a header that Handanovic did well to touch over and Sigurdsson teed-off again from distance, taken by Handanovic to his left.
The only surprise was to see Inter burst through three minutes from half-time as Antonio Cassano's pass deflected off Gallas to allow Alvarez to race through on goal. He had plenty of time to pick his spot - and fired well wide.
Inter made a change at the break as Rodrigo Palacio joined Cassano up front for Juan.
Vertonghen had the first chance of the second half, slicing wide from Bale's free-kick but the defender made no mistake when presented with another gilt-edged opportunity. This time, Bale swung in a header from the right and Vertonghen planted his header home from six yards.
Bale drove past defenders into the box for the next chance on the hour, his low shot clipping the post.
Defoe was soon wondering how his low shot was kept out by Handanovic. Rolled in by Scott Parker, the striker let fly in his stride and the shot appeared to beat the goalkeeper's initial dive, strike in the inside of his right hand and wide.
Parker set up the next chance with a quick burst from central midfield, this time slipping the pass into Lennon. The winger drifted slightly wide and that allowed Handanovic to make another fine save.
There was a warning at the other end on 74 minutes as a quick free-kick found Palacio in front of goal but Friedel was there to make a crucial block with his feet.
The next chance came from an unlikely source as Gallas broke forward. He played a couple of one-twos before finally finding substitute Lewis Holtby, his strike deflected straight at Handanovic.
That typified the performance - and another glory, glory night in Europe at the Lane.
Spurs (4-4-2): Friedel; Walker, Gallas, Vertonghen, Assou-Ekotto; Lennon (Naughton, 82), Dembele (Livermore, 64), Parker, Sigurdsson (Holtby, 71); Bale, Defoe. Unused subs: Lloris, Caulker, Dawson, Naughton, Carroll.
Inter Milan: Handanovic; Zanetti, Chivu, Ranocchia, Juan (Palacio, 46); Cambassio, Gargano; Alvarez (Jonathan, 67), Kovacic (Guarin, 56), Pereira; Cassano. Unused subs: Belec, Benassi, Pasa, Mbaye.
Yellow cards: Spurs - Bale. Inter - Guarin, Pereira.
Goals: Spurs - Bale (6), Sigurdsson (18), Vertonghen (53).
Referee: Mr A Lahoz (Spain).