Spurs dominated first-half proceedings at St Mary's and deservedly went ahead after 15 minutes courtesy of a Gareth Bale header.
Clint Dempsey doubled the north Londoners' advantage six minutes before the half-time break, which Southampton returned from reinvigorated.
Jay Rodriguez reduced the deficit but Saints were unable to find an elusive leveller as Tottenham held on for a victory Villas-Boas dedicated to football administrator Alex Carroll following the death of his mother.
"He is a person that represents a lot to the team so we wish him the best and hope he recovers from his great loss," the Tottenham manager said.
"Obviously I am happy for what we did in the game and certainly it was a good first half.
"We kept the ball well, managed to create lots of opportunities and always looked in control of the game.
"I am extremely happy for that and what we spoke about at half-time was that only a 3-0 scoreline would put a game like this to bed because Southampton had nothing to lose.
"They came out very, very strongly in the second half. As soon as they scored, the game changes and makes it more difficult.
"It was very, very similar to the game we played at Old Trafford when we had an extremely good first half in terms of keeping the ball and playing.
"But in the second half we showed that desire to defend and hold onto the result."
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It was a quick turnaround for Tottenham, who were involved in a tough 1-1 Europa League draw at NK Maribor on Thursday.
"We came back late from our trip against Maribor," Villas-Boas said.
"We arrived at 2am in the morning, had two days to recover to play a game like this.
"It required big physical capability and the players really put in the effort.
"It shows a good example of the possibility that you have to play in the Europa League, be available for the Premier League and still be able to win games."
Bale was one of several players not travel to Slovenia, although it was the birth of his first child rather than injury that saw him remain at home.
The Wales international returned to the fold today [Sunday] against the side he began his career with and impressed in the first half at his old stomping ground.
"I am extremely happy for him," Villas-Boas said. "He is a massive player for the team.
"He is a player that can make a different with small opportunities.
"He certainly did that today and scored. It was good for him to be back on the scoresheet.
"He is certainly someone we rate very, very highly and can go all the way to becoming one of the best."
Today's result moves Tottenham up to fourth but leaves Saints with just four points to show from their opening nine matches.
"The second half was very good," Southampton manager Nigel Adkins said.
"We gave ourselves an opportunity to win the game and what we did in the second half we actually wanted to do in the first.
"Let's give Spurs a little bit of credit because they slowed the game down very well from that point of view.
"They passed the ball and I think we had good possession of the football up until the final third, but just could not find a breakthrough.
"That is something we spoke about at half-time but in the second half it was a good performance from the players."
As well as defeat, another negative point was an apparent altercation between Artur Boruc, making his home debut, and the Southampton support after Spurs' second goal.
"Pass, I am totally unaware of it," Adkins said. "I am not aware of any incident going on."