Pompey's former England goalkeeper was barely 60 seconds from moving ahead of David Seaman in the all-time charts with his 142nd shut-out.
But then Fulham defender Ian Pearce tried a hopeful shot that cannoned off Linvoy Primus to leave James on one side of the net with the ball in the other.
It was so tough on James and on Pompey boss Harry Redknapp who thought his team were going to push their way back into the fight for European places with their first away win since Boxing Day.
They grabbed the lead after barely four minutes when Croatian midfielder Niko Kranjcar caught Antti Niemi off his line and curled a delicious shot beyond his reach into the top corner from 25 yards.
It was the first goal the youngster, son of his country's World Cup boss Zlatko, has scored for Pompey since his arrival last summer and prove of his growing status as a fine Premiership player.
But Pompey didn't really build on the early goal, and Fulham fought back with a determined display.
Their spirit was typified by Pearce, who should really have gone off early in the second half when he was hurt making a desperate last-ditch tackle to stop Benjani increasing Pompey's lead.
But boss Chris Coleman had already used all three subs in an effort to shake his team up, and the 32-year-old defender fought on for the sake of his team.
He needed fully five minutes treatment before returning to the field, and then had to spend another ten minutes hobbling about up front while he ran off the injury.
And just when it seemed his efforts would be in vain he moved forward to take his chance after Pompey defender Lauren failed to clear after a wriggling run by Alexei Smertin.
It was tough on James, who had made several outstanding saves to show that it had not just been luck that he equalled Seaman's record a fortnight ago - and that he will go on to set the benchmark even higher.
The best of them was to push away a curling left-foot effort by Smertin, but he also dived bravely at the feet of Fulham sub Vincenzo Montella.