The two Premier League giants went into the game at Anfield with United in fourth place, two points above their opponents in the race for UEFA Champions League qualification.
Juan Mata's brace - either side of Steven Gerrard's dismissal for stamping on Ander Herrera within a minute of coming on as a substitute - earned the points for United, with Daniel Sturridge's goal and Wayne Rooney's penalty miss adding further late drama.
With eight Premier League games to go, Van Gaal's side now have a five-point cushion over Liverpool and appear in good shape to return to European football's premier club competition.
"It is the moment that we are coming back and we beat Liverpool again," Van Gaal said.
"They were in a fantastic shape and we beat them with their own weapons, with pressure on the ball in the first half.
"And now the gap is one point [behind Arsenal], five points ahead of Liverpool and six ahead of Tottenham and Southampton.
"The moment to win is important. One of most important moments of my career, I think.
"There are still eight matches to go. When you are a very good top player or top manager or top club that Liverpool is, then you have to deal with defeat.
"Manchester United has also dealt with defeat, Arsenal in the FA Cup at home. We never lose at home and then we have to play against Tottenham and Liverpool away.
"You have to manage that as a player, as a manager, as a club and Liverpool can do that also."
