Mauricio Pochettino's team headed to Old Trafford aiming to pull level on points with their fourth-placed opponents in the Premier League but found themselves on the receiving end of a rampant display from the hosts.
Marouane Fellaini, Michael Carrick and Wayne Rooney all scored before half-time to banish memories of Monday night's abject FA Cup quarter-final defeat to Arsenal.
"We have waited a long time for such a victory," Van Gaal said.
"The performance was very good against a very good team so I am very pleased.
"I have to see the video again, you have to always see the game a second time, but I have to say that we played like a team - very determined and that is nice after a defeat against Arsenal.
"This was a massive, important game after the defeat against a competitor. So I'm very pleased with the players.
"We have played very well, I think. We have played very compact against Tottenham Hotspur and they had a lot of problems with that.
"I also think that they could not give passes so easily to Harry Kane so that makes it more difficult for him."
Heading into next weekend's eagerly awaited showdown with fifth-placed Liverpool, United sit a point behind Arsenal in third and only two shy of local rivals Manchester City - whose ailing title defence suffered another hammer blow when they lost 1-0 at Burnley on Saturday.
"Maybe this is the game that gives us a massive boost," Van Gaal said. "We have to go step-by-step, it is a rat race.
"We are two points from the second position and the next game, as you know is Liverpool.
"Arsenal is one point behind and we are two points behind."
Rooney made pre-match headlines owing to coverage of a video that emerged of himself and Stoke City full-back Phil Bardsley engaged in a mock boxing bout at the England and United captain's home.
Van Gaal decried coverage of the story and paid tribute to a speech given to the players by his skipper on the eve of the Tottenham match.
"The players know that this game was massively important so I think that a captain has to do something to help the players, help the manager and help the club," he added.
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