The Cottagers, flying high in the Premiership, were without the influential Louis Saha and Luis Boa Morte for their first major European encounter, which limited their firepower before the game even started.
Hadjuk Split, joint second in the Croatian Championship after seven games, took control of the match straight from the kick-off and could have taken the lead inside two minutes.
Vlatko Dolonga rose above the Fulham defence to reach Dario Srna's corner but fluffed his header. Fulham then had their first attack of the game but Steve Marlet's shot was charged down.
Split's players appeared eager to go to ground after the faintest challenge as one such moment of acting from Mario Carevic, after making little contact with Andy Melville inside the penalty area, deservedly earned him the game's first booking for a blatant dive.
The hard-working Edwin Van der Sar superbly demonstrated his match-winning qualities in the 29th minute with a fantastic point-blank stop.
Carevic swung over a cross from the left and Srna easily out-jumped Rufus Brevett to power a header goalwards but Van der Sar was equal to the effort and parried the ball away and then retained his composure to cover the follow-up effort that struck the outside of the post.
Gradually the Cottagers gained a foothold in the match and, after making it to half time, they came out the stronger side after the break.
In the 51st minute Fulham turned the game with a clinical Malbranque strike to take the lead. Junichi Inamoto delivered a perfect ball to Marlet, 30 yards from goal, and he slipped it to Malbranque. The former Lyon star beat Pletikosa from 14 yards with a rifled shot into the bottom right-hand corner of the net.
For the rest of the match the home fans showed their displeasure as there was no doubt that Fulham would hold on to win, proving that Tigana's aim of Champions League football within two seasons may not be as ambitious as first thought.
Hajduk Split: Pletikosa, Djolonga, Vejic, Neretljak, Vukovic, Andric, Srna, Racunica, Miladin, Carevic, Deranja.
Subs: Runje, Butorovic, Piric, Radeljic, Bule, Brgles, Gudelj.
Fulham: Van der Sar, Brevett, Goma, Ouaddou, Melville, Inamoto, Davis, Malbranque, Legwinski, Hayles, Marlet.
Subs: Taylor, Clark, Sava, Collins, Knight, Wome, Stolcers.
Referee: Fernando Mendez (Spain)