The Goodison faithful seemed stunned to be watching their first home match for nearly a month and the travelling band of 200 Pompey fans easily out-sang them and had plenty to cheer about.
It was the visitors who created the first chance of the game when Everton's defence were caught napping.
An unmarked Dario Silva collected the ball just inside the area and unleashed a quick right footed effort which Nigel Martyn struggled to get his hands on.
The rebound fell in front of the Blues' open goal mouth but Mikel Arteta managed to scramble it out for an uneventful corner.
But Pompey were on the march again moments later when Brian Priske, who was a constant bright spark on the right wing, linked up well with Gary O'Neil.
However, his short range shot was blocked by David Weir.
O'Neil was gifted the best chance of the first half again by Priske when he slid a death ball through two Blue shirts to be met on the edge of the area, but the effort drifted well wide of the mark.
Everton's build-up play often looked uncoordinated and stunted as they easily coughed up possession and passes meant for the wingmen sailed out of touch.
The Blues' one ray of light was Tim Cahill, who kept his head and created Everton's only real chance of the first period.
He crafted a stealthy pass through the midfield towards Ferguson but his shot bounced over the bar.
And the Aussie international also won Everton a free kick going forward with his constant hustle and determination.
The Blues were lucky not to have gone into the break a goal down, if it wasn't for the intervention of Martyn's crossbar.
Lomana Tresor Lua Lua picked up the ball ten yards outside the area and without looking up fired a thunderous right-footed effort which the Toffees' goalkeeper had no chance of reaching.
Whatever manager Moyes said to his troops over the half-time oranges it had no effect on their play.
Their build-up play maintained a lacklustre pace as they looked content to sit back and defend in their own half.
Everton's lack of passion was punished on 60 minutes when they conceded a soft goal.
Pompey won a corner and as Laurent Robert stepped up for the kick Everton rallied every man except Marcus Bent to defend it.
And it proved a costly mistake as Robert's swinging cross was met by the towering head of blundering Scotsman Ferguson and it sailed into the back of the net for an own goal.
The Blues were left reeling by the goal, but Portsmouth failed to capitalise further as the game descended into a midfield quagmire.
Moyes will need to do some serious rethinking about his team's chemistry before his next game.
Everton are heading for the most disastrous start to a campaign in recent years and need to break their goal drought with some well crafted play which was not seen this time.
Man of the Match: Lomana LuaLua - Gave a superb all-round display that worried the home defence throughout the game and almost got his reward with a first-half goal.