The Gunners, much changed ahead of the second leg of their Champions League clash with holders United, were helped on their way when England goalkeeper David James made his latest high-profile mistake by letting Nicklas Bendtner's weak header slip through his fingers.
Danish striker Bendtner made it 2-0 four minutes before half-time from the penalty spot following a disputed foul by Sean Davis on Andrey Arshavin.
Pompey were punished for missing chances early in the second-half when Carlos Vela added a third Arsenal goal and the hosts then saw Noe Pamarot sent-off for a foul on Arshavin.
Manchester City left Blackburn Rovers nervously looking over their shoulders after a 3-1 win at Eastlands where South American trio Felipe Caicedo, Robinho and Elano all scored before the break.
Caicedo sent City on their way from the edge of the six-yard box before Robinho added a second with a shot that gave keeper Paul Robinson no chance.
Elano made it 3-0 from the penalty spot after handball in the box before Rovers pulled one back through Keith Andrews.
Elsewhere, Tottenham beat bottom-of-the-table West Brom 1-0 thanks to Jermaine Jenas's 25-yard curling shot while Diego Tristan's free-kick from a similar distance gave European contenders West Ham a 1-0 win away to Stoke.
