Ryan Giggs also struck for the champions who now have 31 points from 14 games, two behind Chelsea who play at third-placed Arsenal (25 points) on Sunday.
Tottenham Hotspur drew 1-1 with Aston Villa at Villa Park in the late game to leapfrog Arsenal and go third in the standings on 26 points, while Manchester City remain sixth on 22 after they were held 1-1 at home by struggling Hull City to record a Premier League record seventh successive draw.
West Ham United beat Burnley 5-3 while Wigan Athletic bounced back from last week's 9-1 hammering at Spurs by beating Sunderland 1-0.
Rooney earned the headlines with his treble but in truth the England striker, along with several of his United team-mates, otherwise had a quiet game.
Portsmouth, who have beaten United and drawn with them at Fratton Park in the last two seasons as well as knocking them out of the FA Cup at Old Trafford last year, were the better team for much of the first half in their first game under manager Avram Grant following the midweek sacking of Paul Hart.
However, they paid for missing several good chances when United went ahead with a Rooney penalty in the 25th minute after he had been brought down by Michael Brown.
The referee evened things up seven minutes later with another hotly debated penalty award when he decided Frederic Piquionne had had his shirt pulled and Kevin Prince Boateng scored from the spot.
SOFT GOALS
"It was a strange game because if you analyse it you can say it was a good game for us. We created a lot of chances and conceded soft goals," Grant told Sky Sports.
United looked far livelier after the break and neat work by Giggs, who turns 36 on Sunday, set up Rooney for his second.
The third penalty of the match was awarded for a foul on Giggs in the 54th and Rooney duly converted for his hat-trick before Giggs rounded things off with a late free kick to register his 100th Premier League goal.
United's ability to win comfortably without hitting top form is in marked contrast with cross-town rivals City, whose top-four aspirations recede with every passing stalemate.
They went ahead with a deflected long-range shot by Shaun Wright-Phillips at the end of the first half but Hull battled throughout and grabbed a point with a Jimmy Bullard penalty eight minutes from time.
"Today I sensed a little bit of anxiety in our play. We've been in this situation of giving away a winning position. On the day a draw was probably all we could ask for," City manager Mark Hughes said.
Villa went ahead after 10 minutes courtesy of Gabriel Agbonlahor's close-range strike, though the home side lived dangerously at times and Spurs deservedly equalised with a thumping drive by defender Michael Dawson after 77 minutes.
West Ham, who had managed only one home win before Saturday, were grateful to be playing a Burnley side who had lost five and drawn one of their six away games.
The Londoners went ahead through Jack Collison, added a second th
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