They took the lead when Eduardo’s free-kick deflected in off Younes Kaboul, before Samir Nasri fired in a second.
Aaron Ramsey made it 3-0 with a brilliant solo goal, hammering in from 20 yards, before Nadir Belhadj’s close-range strike gave Pompey faint hope.
But Alex Song superbly headed in a Nasri cross to wrap it up for Arsenal.
Arsene Wenger’s men keep up the pressure at the top, moving to within four points of Chelsea and staying two behind Manchester United with a game in hand on each.
The final round of Premier League fixtures of the year also contained a first for the top division – neither side fielded an Englishman in their starting XI at Fratton Park.
Wenger revealed before the game Arsenal would be without influential captain Cesc Fabregas for two weeks, but they never looked like they needed the brilliant Spaniard against the league’s basement boys.
Try as they might, Portsmouth simply could not compete and it completed a difficult day at the office after they had earlier been issued with a winding-up petition by HM Revenue & Customs (HMRC).
Cut four points adrift at the bottom, Pompey were desperate for an early morale boost after going down 2-0 at West Ham on Boxing Day, but save for a Kevin-Prince Boateng shot that Manuel Almunia parried away, they all-too-rarely threatened.
As they tend to do, the Gunners enjoyed the lion’s share of the possession and they worked the hosts around their own pitch as their superior passing game made Portsmouth toil.
Soon the chances began to arrive as Andrey Arshavin hammered over, Eduardo glanced a header wide and then Asmir Begovic pulled off a superb reflex save from Abou Diaby’s near-post shot.
It was a matter of time before Arsenal went in front, and when Aaron Mokoena hauled down Ramsey 25 yards out, they seized their opportunity.
Eduardo’s left-foot shot took a deflection off Kaboul to wrong-foot Begovic and Hermann Hreidarsson – standing on the line – simply stood and watched the ball fly past him into the corner where he should have been standing.
Just before the break a lovely Arsenal move led to Eduardo finding space in the area and he was given an age to pick out Ramsey – the Welshman then neatly teeing up Nasri to belt home from 16 yards.
The gulf in class remained stark after the break, though the Gunners had to wait until 20 minutes from time to add to their goal tally.
It was worth the wait, though, as Ramsey dispossessed Anthony Vanden Borre, effortlessly skipped past Frederic Piquionne and slammed a stunning left-foot shot into the corner from just outside the box.
Pompey had a glimmer of hope when Belhadj’s shot from Vanden Borre’s pass deflected in off Thomas Vermaelen, but the visitors soon restored their three-goal cushion as Song strained his neck muscles to powerfully head home Nasri’s right-wing cross.
Arsenal, who have now scored 51 goals in 19 Premier League games this season, end the year on a high after three successive wins, but Pompey face an uncertain future both on and off the field.