Villas-Boas handed Defoe his first start of the season against Dinamo Tbilisi and he responded in style by scoring twice in a 3-0 win which puts the London club in to the hat for Friday's draw.
Defoe has been edged out of the first-team reckoning thanks to the excellent form of B£26million record signing Roberto Soldado, who has bagged four goals in three games.
That has led to renewed speculation that Defoe could be on his way out of White Hart Lane before the transfer window shuts on Monday night, but Villas-Boas insists the 30-year-old is going nowhere.
"I think he will be here after the closure of the transfer window," the Tottenham manager said. "He has delivered the goals when we wanted. He has come on in the last two Premier League games and he has done extremely well for the team.
"He is a great professional with a great attitude and today he delivered a great performance.
"At the moment, we have played with one striker and Jermain and Soldado are competing for that spot with (Emmanuel Adebayor) out. There is competition and I think that is what is created in any big team."
Lewis Holtby wrapped up the game in the second half with his first goal for the club - a fine 20-yard strike which cannoned in off the underside of the crossbar.
Villas-Boas was happy with his team's professional performance following their 5-0 first leg win in Georgia last week.
"It would have been very easy to be complacent and we weren't," the Tottenham manager said.