United's second win of the season over Arsenal took its unbeaten record against the Gunners to five matches and pushed the defending champion to 53 points.
Arsenal, which only scored with 10 minutes left when Thomas Vermaelen's shot deflected off defender Jonny Evans, is in third place on 49 points after its first Premier League defeat since November.
Manchester City is eight points back from Arsenal in sixth place after beating last-place Portsmouth 2-0, although City could easily climb higher since it has played two fewer matches than the four sides immediately above it.
Arsenal was expected to give United a tough match in north London and Andrei Arshavin's attempts to isolate Wes Brown, who was playing alongside Jonny Evans in central defense because of the absence of Rio Ferdinand and Nemanja Vidic, gave the Gunners early hope.
But United took control with its 33rd-minute opener and could have won by a bigger margin, with Nani and Rooney both going close to scoring more.
Arsenal only managed to exert sustained pressure on United in the last 10 minutes.
Nani created United's first goal when he danced between two defenders on the right touchline, dodged a third on the edge of the area and floated a cross from a narrow angle toward the far post.
With Park rushing in behind for what would have been an easy finish, Almunia tried to flick the ball over the bar but pushed it into the net.
Nani then played an integral role in the length-of-the-field counterattack that ended with Rooney calmly shooting past Almunia for his 100th Premier League goal.
Arsenal's defense disintegrated as Park charged from inside his own half to score before Vermaelen finally roused a dispirited home crowd with his late goal.
United has now won three straight Premier League matches and is in strong contention for a record fourth straight title, despite rarely hitting top form this season after the sale of Cristiano Ronaldo to Real Madrid.
Arsenal needs to rally quickly, but has matches against Chelsea and Liverpool up next.
Emmanuel Adebayor and Vincent Kompany scored first-half goals to put Manchester City level on points with Liverpool and just one point behind fourth-place Tottenham.
Portsmouth, which sold another key player Saturday to further alleviate the financial problems threatening its future, remained last in the standings with 15 points - five fewer than the next worst side and without a league win in six weeks.
Adebayor put City ahead in the 40th minute, taking one touch on Stephen Ireland's perfectly placed pass from halfway and smashing a half volley past England goalkeeper David James.
Kompany made it 2-0 five minutes later with a firm header from Martin Petrov's corner.
Chelsea beat Burnley 2-1 on Saturday to keep the lead on 54 points, while Tottenham drew 1-1 at Birmingham and Everton's resurgence continued with a 1-0 win at Wigan.
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