United have 74 points with six matches left and Liverpool, who drew 4-4 at home to Arsenal [ Images ] on Tuesday, have 71 with five games remaining. Chelsea are on 68 having played a game more than Alex Ferguson's [ Images ] side.
After sitting out United's penalty shootout defeat by Everton in the FA Cup semi-final on Sunday, Rooney and Cristiano Ronaldo [ Images ] returned for United as they set about seizing control of the league and they were given the perfect start.
Anderson released Ryan Giggs [ Images ] down the left after nine minutes and the veteran winger, as he has done throughout his career, picked the perfect pass to allow Rooney the simplest of finishes.
John O'Shea and Giggs both missed chances to stretch the lead before halftime against an unadventurous Portsmouth side who created little threat.
There were still a few jitters around Old Trafford, however, until Carrick made the points safe, supplying a polished finish to a ball from midfielder Paul Scholes who was making his 600th appearance for the club.
However, injuries to right backs Gary Neville [ Images ] and John O'Shea will be a concern for Ferguson.
At Stamford Bridge, sixth-placed Everton were the better side in the first half with Brazilian striker Jo twice unable to cash in after being put through on goal.
The closest Chelsea came to a winner in a rehearsal for next month's FA Cup final was a Didier Drogba [ Images ] shot against the crossbar three minutes into stoppage time.