Champions United, inspired by a superb performance from Wayne Rooney, beat Wigan Athletic 5-0 at Old Trafford while Arsenal were never troubled by bottom-of-the-table Portsmouth in a 4-1 win at at Fratton Park.
Chelsea, who completed their holiday fixtures with a 2-1 win over Fulham on Monday, lead the table with 45 points from 20 matches, followed by United on 43 and Arsenal on 41 with a game in hand.
Tottenham Hotspur complete the top four with 37 points from their 20 games. United, who had beaten Wigan in all 10 of their previous matches, were certain of making it 11 out of 11 by half time as they raced into a 3-0 lead with goals from Rooney, Michael Carrick and Rafael da Silva.
Dimitar Berbatov and Antonio Valencia scored in the second half.
Arsenal, who have not lost to Portsmouth since 1958, also had the points wrapped up by the break, thanks to goals from Eduardo and Samir Nasri.
Aaron Ramsey made it 3-0 after 68 minutes with Arsenal's 50th league goal of the season and Alex Song Billong headed a superb fourth nine minutes from time, after Nadir Belhadj had netted a consolation for the home side.
The results left Wigan struggling two places and one point above the relegation zone, while Portsmouth remained bottom with 14 points from 20 matches -- four points adrift of Hull City, Bolton Wanderers and West Ham United.
At Old Trafford, United took control from the kick-off and the only surprise was that it took 28 minutes for Rooney to open the scoring, planting the ball in at the near post.
Carrick completed a sweeping move with a low shot for the second before Da Silva struck on half-time with an arrowed shot from the edge of the box for his first of the season.
Manchester United manager Alex Ferguson said he was delighted that defenders like Nemanja Vidic and Wes Brown were fit again after injury because their return would improve the team for the second half of the season.
"Vidic and Brown coming back makes a tremendous difference to the team," Ferguson said. "When we get all the defenders back, come the second half of the season we will be a much better team."
Despite the absence of injured skipper Cesc Fabregas, Arsenal were also in control from the start at Fratton Park, where the day began badly for the hosts after they were ordered by Britain's tax authorities to pay the money they owed or be taken to court in the New Year.
Portsmouth were soon in debt on the pitch too, falling behind in the 28th minute when Eduardo's free-kick took a deflection off Younes Kaboul and bounced over the goalline.
Nasri scored his first of the season to put Arsenal 2-0 up with a well-taken chance in the 42nd minute after a neat Arsenal move, aided by some woeful Portsmouth defending.
Ramsey scored the third with a crisp drive before Alex Song Billong headed their fourth nine minutes from time.
Arsene Wenger told Sky Sports he believed Arsenal were good enough to win the title for the first time since 2005.
"We are up for it 100 percent," he said. "The commitment is there, the focus is there and the talent is there so it will be very interesting.
“We will fight for it. This team is ready to give absolutely everything.
"We believe, and if we don't believe, nobody will believe."
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