With the race for a top-four finish in the Premier League becoming increasingly tense, United struck a potentially decisive blow with goals from Juan Mata in each half helping them move five points clear of Liverpool in fourth place.
United were the better side for most of encounter and Van Gaal said the victory was forged from playing Liverpool at their own game.
"They were in fantastic shape, but we beat them with their own weapons -- the pressure on the ball," Van Gaal told reporters, referring to the relentless pressuring of the ball that Liverpool boss Brendan Rodgers has made his trademark.
"The gap is one point behind (Arsenal in third), five ahead of Liverpool, six to Tottenham and Southampton; the moment was very important, one of the most important of my career."
Liverpool trailed United by 10 points after losing the reverse fixture 3-0 in December but had dragged themselves back into contention with an unbeaten run in the intervening period.
United's victory, however, has left Liverpool again playing catch-up although Dutchman Van Gaal said they were not yet dead and buried.
"When you are top club, manager, players -- and Liverpool is -- you have to deal with defeat. Liverpool can do that," he said.
United managed to stifle Liverpool entirely in the first half and made the most of their superiority, opening a two goal lead with goals either side of Steven Gerrard's 38-second sending off for stamping on Ander Herrera.
While the hosts clawed a foothold in the match with a Daniel Sturridge goal with 20 minutes to play, they never looked like snatching a leveller as United put in arguably their most accomplished performance of the season.
Van Gaal, however, was only partially satisfied.
"It was the best first 45 minutes," he said. "But in the second half we were not so good.
"Then we played eleven against 10 and it should have been easier but it was not.
"But the first half was very good because I knew Liverpool would press us, and they did, but we played them off the pitch, scored a fantastic goal and gave nothing away."
(Reporting by Toby Davis; Editing by Ian Chadband)
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