The tie is currently poised at 2-2 following a thrilling encounter at White Hart Lane last week in which strikes from Adebayor and Gylfi Sigurdsson overturned a two-goal deficit.
And, after the Togolese striker netted and hit the post in Sunday's draw with Everton, Villas-Boas is backing him to play a big role in Switzerland.
"Adebayor has got back in the goals in our recent games and he has shown how influential he can be," the 35-year-old told reporters.
"He's a player who is really enjoying his football; he is driven by his last goals and last performance and he is doing extremely well.
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"Finding the back of the net allows him to go into the game with more confidence and I always think it's self-belief from the player, rather than anything else, that helps them improve.
"His link-up play has improved tremendously. He's been much more involved in the build of play and assisted and created so much, allowing others to flourish. He has helped Aaron Lennon and Gareth Bale improve their game."The Portuguese boss went on to insist that playing away from home will not be a factor to his side if they play "with ambition".
"Football is a surprise. What we have to do is get focused tomorrow to win the game, play with ambition to reach a prestigious semi-final after so many years for Tottenham," he added.
"That should be motivation to drive us through. Our home form has dipped a little bit but our away form in the Premier League has been excellent and I'm sure it will serve as an inspiration for us.
"Normally we feel very comfortable away from home."