Al Fahim did not arrive at Fratton Park until ten minutes after kick-off, having jetted in straight from New York on Saturday morning.
The Dubai billionaire took his seat in the directors' box just in time to see Zamora give Fulham a 13th minute lead.
Clint Dempsey took aim from 25 yards but the American's low shot was heading straight into David James' arms before the ball struck Zamora and trickled into the bottom right corner.
Zamora would have added a second moments later but for a fine fingertip save from James to turn the former West Ham striker's close-range header over the crossbar.
Hart has been forced to sell England duo Peter Crouch and Glen Johnson to reduce debts and has released ten other players including captain Sol Campbell.
It took until the 24th minute for Pompey to test Fulham goalkeeper Mark Schwarzer when new French signing Frederic Piquionne turned neatly on the byline before putting a snap-shot into the Australian's arms.
The home side, reportedly facing the prospect of going into administration if Al Fahim's takeover falters, should have been level on the half-hour when Niko Kranjcar whipped in an inviting right-wing corner, but the unmarked Nadir Belhadj somehow failed to make contact with an attempted diving header.
Portsmouth's summer of turmoil has clearly left supports disillusioned and a crowd of just 17,510 is the south coast side's lowest league gate in two years.
Maybe Andy Johnson was feeling sorry for the home fans when he passed up a golden chance to make it 2-0 midway through the second half after blazing over the crossbar after being left totally free eight yards out.
Younes Kaboul's header which flew two yards wide from a late Belhadj corner was the closest the hosts came to snatching a point they would not have deserved.