Jan Vertonghen opened the scoring early in the first half before Jermain Defoe sealed the victory, Spurs' fifth in a row in Europe - though Sheriff had plenty of chances of their own to score.
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"We had to work hard for this win," said the Portuguese. "We went through a moment of the game where we could have suffered. The second goal gave us stability.
"We have nine points now which is a completely different position to where we were last year.
"The objective was to secure qualification over the course of these two games and this result ensures we still have that possibility."
Defoe's 75th-minute goal was his 22nd in Europe, equalling former Spurs player Martin Chivers' club record which has stood for over 40 years, and Villas-Boas was quick to praise the diminutive frontman.
"It's a great achievement," the Spurs boss added. "We'll celebrate even more if he overtakes the record."