Bobby Zamora gave the visitors the lead but Alejandro Faurlin's own-goal was quickly followed by a Jermain Defoe strike that proved enough to seal three points and Villas-Boas' first home win in charge of the north London club.
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Villas-Boas revealed that he asked his players to match the desire of Mark Hughes' team after a difficult first half, but praised their response.
"You could almost feel the anxiety in the stadium when we went 1-0 down in the first half," he told reporters.
"QPR dominated in the first half and we needed to be more aggressive and play with more desire.
"The players understood that and really put on a show in the second half. It was so important for everyone and we fought hard to get this result."
Tottenham face Carlisle United in the League Cup on Wednesday evening before travelling to Old Trafford to face Manchester United when top-flight action resumes on Saturday.