The north Londoners were in ruthless mood throughout a one-sided first half, Gareth Bale heading the opener before Gylfi Sigurdsson capitalised on more sloppy Inter defending to double the lead.
Andre Strammacioni's men continued to look shaky at the back in the second period, and Jan Vertonghen was left all alone to easily nod in a third from a corner before the game wound down.
Villas-Boas said afterwards: "It was a full 90 minute performance with excellent attacking football. We tried to limit their chances and had so many opportunities. It was a great European night.
"Unfortunately, we're not through yet because we have to go there and the San Siro is a very difficult place to go."
The one blot on the evening for Spurs was a booking for Welsh wizard Gareth Bale - his caution for diving meaning he will miss the second leg in Milan.
Villas-Boas added: "It's difficult but with this result, if he hadn't have got the card it would not have cleared him. We took a risk, obviously but we have talent throughout the squad.
"We have now allowed Gareth to clean his yellow cards and hopefully we can make it through (without him)."
Bale himself said: "We immediately made it difficult for them, it was a great performance and a worthy result to be honest.
"It's always nice to get a goal however it comes and I'm enjoying playing. It was a great performance and we take a great lead into the away leg with no away goals for them."