Radamel Falcao produced a fine piece of skill to turn John O’Shea in the box and was hauled down by the Sunderland defender to earn United a second-half spot-kick.
Brown did not appear to make any contact with Falcao, but referee Roger East showed him a straight red card before Rooney drilled in the penalty on 66 minutes.
Rooney then added his second – and first from open play in 2015 – by heading in from close range with six minutes left when Costel Pantilimon parried Adnan Januzaj’s shot. Januzaj had replaced the disappointing Angel di Maria at half-time.
Ander Herrera had a late goal correctly ruled out for offside but the result leaves Sunderland three points above the relegation zone and with just one win in their last 10 Premier League matches.
United began the game brightly and Rooney – who had gone eight games without a goal before kick-off – wasted a good chance to open the scoring four minutes in when he headed Di Maria’s corner wide.
However, Sunderland showed early intent too, with Connor Wickham surging forward and drawing a fine save from David de Gea from the edge of the box before Jermain Defoe curled a shot over the bar.
United dominated possession throughout the opening 45 minutes though, and the impressive Ashley Young sent a powerful volley over the bar before his cross-shot deflected up onto the woodwork off the foot of O’Shea.
The impressive Young – who caused Anthony Reveillere problems throughout the match – then cut inside and bent an effort wide from 25 yards before Sebastian Larsson hacked Marcos Rojo’s effort off the line five minutes before the break.
Di Maria had a first half to forget, wasting numerous opportunities to deliver a good cross into the box, and was replaced by Januzaj at the interval.
The young Belgian had an immediate impact, winning two corners at the start of the second half before lashing a volley wide on the hour mark when Reveillere half-cleared Rooney’s free-kick.
Well-organised Sunderland continued to frustrate United until a smart piece of control from Falcao – who started in place of the injured Robin van Persie – left O’Shea little option but to foul the United striker in the area.
However, controversy followed when the referee – advised by his assistants – showed a red card to O’Shea’s fellow centre-back Brown before Rooney fired the penalty low past Pantilimon’s right.
Substitutes Januzaj and Marouane Fellaini both tested the Sunderland shot-stopper as tiredness took its toll on the visitors before Rooney nodded in the second from close range to put the result beyond doubt on 84 minutes.
There was still time for one more moment of drama, when Herrera’s injury-time goal was rightly ruled out for offside, after Fellaini had spurned a golden opportunity to score a one-on-one chance.
SOCCER SATURDAY VERDICT – PAUL MERSON
“It was comfortable from about 20 minutes after half-time and I have to give credit to Manchester United. I have been a bit harsh on them this season but I thought they did very well. They gave the ball away very cheaply in the first 15 minutes when Defoe had a shot and should have done better; Wickham should have passed to Defoe but chose to shoot. After that they were dominant, United passed the ball quickly, Ashley Young was very good. United got the penalty in the second half, and it was a stonewall penalty. I do not know how the referee got the decision wrong. It was definitely John O’Shea who committed the foul. O’Shea even admitted it was him and not Brown. Everybody makes mistakes, but that was a bad one.”
Man Utd: De Gea (7), Evans (6), Rojo (6), Smalling (7), Valencia (6), Blind (6), Herrera (6), Rooney (7), Young (8), Di Maria (4), Falcao (6). Subs: Fellaini (6), Januzaj (7), Mata (6).
Sunderland: Pantilimon (7), Brown (7), O’Shea (6), Reveillere (6), Van Aanholt (7), Cattermole (7), Gomez (6), Johnson (6), Larsson (6), Wickham (6), Defoe (6). Subs: Vergini (6), Fletcher (6), Graham (6).
Man of the match: Ashley Young