The club had earlier issued a statement denying being formally served with a winding up petition by Her Majesty's Revenue and Customs in respect of disputed VAT, PAYE and National Insurance contributions of a reported £3.5million.
While that matter may yet be resolved in a High Court hearing early next month to avoid administration, it is clear Pompey - FA Cup winners last year under Harry Redknapp - face an uphill battle to save themselves from relegation come May 2010.
Arsenal fans, meanwhile, could well have the champagne on ice in anticipation of what may yet prove a vintage year for Arsene Wenger's young Gunners - now just four points behind leaders Chelsea and with a match in hand.
The visitors were always in command after Eduardo's free-kick had deflected off Younes Kaboul, before Samir Nasri drilled in a second just before half-time and Wales teenager Aaron Ramsey smashed home a third on 69 minutes.
Although Nadir Belhadj - one of several Pompey players set to leave for African Nations Cup duty - pulled a goal back, Cameroon midfielder Alex Song nodded in a fourth with 10 minutes left.
Wenger had confirmed before kick-off he expected injured captain Cesc Fabregas to be out for around 10 days with a hamstring problem - meaning the influential Spaniard would miss the FA Cup third-round tie at West Ham this weekend as well as tonight's contest.
Pompey had beaten Liverpool here just before Christmas and started well.
Kevin-Prince Boateng caused problems down the right and fired in a shot from a tight angle which Manuel Almunia beat away at the near post.
However, Arsenal looked dangerous on the break and Andrey Arshavin collected a loose ball before drilling a shot from 20 yards over.
Bacary Sagna's cross from the right was glanced wide by Eduardo, before the Croatian got away down the left and laid the ball back into the path of Abou Diaby, who forced a good save from Asmir Begovic at close range.
Pompey captain Aaron Mokoena fouled Ramsey some 25 yards out in a central position - and it proved a costly error.
Eduardo drilled the 28th minute free-kick low, with the ball deflecting off former Tottenham defender Kaboul and past a static Hermann Hreidarsson on the right-hand post to give the visitors the lead on 28 minutes.
Algerian midfielder Belhadj tried to relieve the pressure with a determined run and angled shot, which flew past the far post.
However, in the 42nd minute it was 2-0 when Song - who will not join up with Cameroon until the New Year - fed Eduardo in the left of the area. He pulled the ball back for Ramsey, who picked out Nasri - and the French midfielder drilled a low strike into the bottom corner.
To their credit, Portsmouth started the second half on the offensive and in the 52nd minute Belhadj flashed the ball across the six-yard box from the left.
The Fratton Park faithful chanted "where's all our money gone?", and cheered when captain Mokoena was replaced by Anthony Vanden Borre.
Hassan Yebda - another African Nations Cup departure - drilled a 20-yard effort straight at Almunia.
In the 65th minute there was a length stoppage as Boateng needed treatment after falling heavily in the Arsenal penalty area.
The Portsmouth fans used the break in play to again vent their anger towards owner Ali Al Faraj as chants of "sack the board'' and "you're not fit to run a club'' rang out.
But, in the 69th minute, the home fans were silenced when Ramsey robbed Vanden Borre and charged past Frederic Piquionne before lashing a left-foot shot into the net from the edge of the box.
The home side at least had something to shout about five minutes later when Belhadj converted a low cross from Vanden Borre.
However, hopes of an unlikely home comeback were ended 10 minutes from time when Song headed in Nasri's right-wing cross.
Burkina Faso is in Group B with Côte d´Ivoire, Ghana and Togo, and plays next January 11th against the Ivoirians.
