The Portuguese coach compared the performance to the 3-2 away win against Manchester United as his team held firm in the face of a second-half onslaught from the home side.
The win, which the manager dedicated to Alex Carroll, one of the club's football administrators whose mother passed away in the days leading up to the match, moves Spurs up to fourth in the Premier League.
"We wish him the best to recover for his great loss," Villas-Boas told reporters of the Spurs employee before going on to speak glowingly of a performance that he compared to the 3-2 win at Manchester United in September. "It was a good first half, we kept the ball well and managed to create lots of opportunities. We always looked in control of the game.
"Only 3-0 would put the game to bed because Southampton had nothing to lose, so they came out very very strong. We could have held onto the lead at 2-0 but as soon as they scored, the nature of the game changes. It was very similar to Old Trafford, where we had an extremely good first half but in the second half we showed that desire to defend and hold onto the result."
The Saints, buoyed by Jay Rodriguez's goal, pressured heavily in the second period and, questioned whether he was pleased with the number of blocks his defense put in, Villas-Boas noted: "When the nature of the game changes, it is that kind of effort you want from your players.
Villas-Boas also reserved praise for Gareth Bale, who scored Tottenham's opener in what was the first game he had played against the club with which he began his career.
"I am extremely happy for him," the Spurs boss enthused. "He's a massive player for the team, someone who in the small opportunities can make the difference. He defended well, scored, and it was good for him to get back on the score sheet and certainly someone we rate very very highly."
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