Man United wasted a number of opportunities to rescue something from the game, while January recruit Martin Dubravka impressed on his debut by keeping out Jesse Lingard, Anthony Martial, Ashley Young and Michael Carrick.
Benitez was pleased with the performance of each of his players, and in particular goalkeeper Dubravka.
"He can buy the lottery and win today. He was composed and that gave confidence to the team," he told Sky Sports News. "All the players worked hard, so it is not fair to say just the goalkeeper played well.
"We worked as hard as other games, but against a team like Manchester United every ball is important, they can punish you, so you work like them. Amazing effort.
"They are dangerous, but the teamwork we showed to fight for every ball was amazing. I am pleased for the players and the fans. Because we won here at home.
"We had games in past when conceded late. We got lucky with some shots, but we showed the character, the commitment and the desire today."
Newcastle move up to 13th in the table with the victory and just three points off the top half.