United effectively had the game won within 16 minutes as they surged into a 2-0 lead without breaking sweat.
First central defender Jonny Evans was allowed to run on to Van Persie's eighth-minute corner and power a header past keeper Steve Harper, and then full-back Patrice Evra applied a similarly comprehensive final touch to Wayne Rooney's 16th-minute corner to extend the lead.
The Scot said: "It was a great result. To come here and win 3-0 against a very powerful, aggressive Newcastle team, you have to really perform and make sure you keep control of the game, and I think we did that most of the time."
"It's strange - we played such good football and made a lot of good openings, but we scored from two set-pieces, which is unusual for us, so we will take it, anyway.
"Patrice, I think has only scored two goals and I think Jonny Evans has only scored two goals."
Newcastle came desperately close to dragging themselves back into it five minutes after the restart when Demba Ba headed Shane Ferguson's cross on to the bar and Papiss Cisse stooped to head the rebound towards goal.
However, keeper David de Gea clawed it on to the post and survived claims that the ball had crossed the line.
Ferguson said: "The goalkeeper has done fantastically, actually, to get to it, but if the rule is the whole ball has got to be over the line, then it's not a goal.
"But I would be disappointed because I thought enough of the ball is over."
Newcastle's misery was complete 19 minutes from time when Tom Cleverley cemented victory with a curling effort from long range, although there was not complete agreement over whether he meant it or not.
Cleverley told Sky Sports: "Yes, I meant to put it in that far corner. I looked to the far corner - whether it's a good cross or it's a good finish, luckily it found the net."