The Reds Devils have now clipped the Magpies' wings three times this season - this win completing a league double a week after United beat Newcastle 4-1 in the FA Cup semi-final.
Yet Newcastle must have thought they had laid the foundations of victory after another goalkeeping error gifted them a 27th minute lead.
Phil Neville's back pass seemed to pose no problems for Tim Howard, but the American keeper, in attempting to find Quinton Fortune five yards outside the box, saw his pass intercepted by Darren Ambrose.
The Newcastle winger touched the ball on to Shola Ameobi and he returned it to Ambrose, who stroked his shot beyond Howard and into the net from ten yards out.
The home side, who lost left-back Gabriel Heinze after he was carried off on a stretcher after 38 minutes when falling badly from an aerial challenge, showed little imagination in the first half.
If they were going to get back into the game after the break they needed something special and that came in the 57th minute.
Peter Ramage headed Roy Keane's long ball from the halfway line into the path of Wayne Rooney 25 yards from goal.
But few people expected the finished product as Rooney, suffering from a dead leg, scored with a vicious right-foot volley which screamed past Newcastle keeper Shay Given and into the top right-hand corner of the net.
Sir Alex Ferguson's side had finally stirred from their slumber and took the lead after 75 minutes.
Ryan Giggs swung his corner into the centre of the Newcastle penalty area were Brown jumped above Ameobi to head home from six yards.
Both sides had good claims for penalties turned down - Newcastle in the 19th minute when Howard floored Alan Shearer and the home side three minutes before the break after Andy O'Brien wrestled Alan Smith to the ground.