Though Chelsea are virtually assured of the title on 85 points, United's victory moved them on to 70, one point behind an Arsenal side who face Tottenham Hotspur in the north London derby on Monday.
Arsenal are anxious to hold on to second place and qualify automatically for next season's Champions League. They also know that failing to beat Spurs at Highbury will make Chelsea champions.
Sunday's other game was a thumping 4-1 win for Portsmouth in the south coast derby against Harry Redknapp's bottom-placed Southampton, who remain prime candidates for relegation after 27 consecutive seasons in the top flight.
Up at Old Trafford, Alex Ferguson's men found themselves unexpectedly behind -- a week after they crushed Newcastle 4-1 in their FA Cup semi-final in Cardiff.
Darren Ambrose gave the visitors a 27th minute lead when he pounced on a poor clearance by U.S. keeper Tim Howard and skipped past two defenders before steering the ball home.
Things went from bad to worse for United in the 39th minute, when Argentine defender Gabriel Heinze was carried off on a stretcher with what looked like a serious ankle injury.
ROONEY STRIKES
But United, who face Arsenal in the FA Cup final on May 21, were lifted just before the hour when Rooney kept his eye on a headed clearance before meeting the ball with a fantastic 25-metre volley into the top corner that gave Shay Given no chance.
Brown's first league goal, a header from a Ryan Giggs corner, secured the win.
Ferguson felt his side were unsettled by Newcastle's goal but told Sky Sports News: "In the second half they (Newcastle) got the bit between their teeth and it took a fantastic goal from Wayne Rooney to change the pattern of the game.
"I was ready to take him off, actually, because he was injured in the first half and he just hobbled on...but whilst he's on the pitch he's such a threat."
Newcastle boss Graeme Souness, whose team have lost five games in three compeititons over the last two weeks, said: "I think we were unlucky today...we had some good performances out there and until they got their first goal we felt quite comfortable."
There was an unhappy return to Fratton Park for Southampton manager Harry Redknapp four months after he controversially swapped clubs on the south coast.
All five goals came in an astonishing opening 27 minutes, helped by two howlers from Southampton keeper Antti Niemi, as his team stayed bottom on 28 points with three games to play.
Portsmouth won a penalty, converted by Nigerian striker Yakubu Aiyegbeni, after just two minutes, Dutch defender Arjan De Zeeuw headed their second and Lomana LuaLua struck twice after Henri Camara had pulled one back for Southampton.
They trail West Bromwich Albion, who have 29 points and face Blackburn Rovers on Tuesday in a game in hand, and Norwich City, who have 30 points and are behind Crystal Palace on goal difference.
"There's no good me going in the dressing room and slating people because their confidence is shot anyway. It has been all season," Redknapp told Sky Sports News. "I've got to lift them and keep believing them in them.
