Fulham started the second half at a frenetic pace and they were ahead just two minutes after the restart.
Popovitch had just fired over the bar from Haka's first attack of the half and Fulham goalkeeper Maik Taylor took a quick goal-kick in search of Marlet. The French forward latched on to Taylor's ball and raced through the centre, before scoring with a low shot from just inside the penalty area.
Haka now needed two goals to go through and, on 66 minutes, they scored. Taylor flapped at a left-wing cross from Lasse Karjalainen and when the ball fell behind the keeper, Ristila was on hand to prod home.
Haka pressed for a winner but the Fulham defence held firm.
Fulham: Taylor, Ouaddou, Harley, Melville, Goma, Legwinski, Davis, Collins, Malbranque, Marlet, Saha. Subs not used: Van der Sar, Sava, Boa Morte, Hayles, Knight, Goldbaek, Stolcers.