The west Londoners endured a frustrating night in Croatia last week as they struggled to a goalless draw in the third qualifying round first leg but managed to see off the Reds on home soil in the second leg.
Andrew Johnson’s header proved the only goal of a first half in which the hosts dominated, before skipper Danny Murphy put the tie beyond doubt from the spot in a challenging second half.
Goran Milovic, Ante Vitaic and Roman Oblinovic all came close to pulling one back for the visitors in the second period, although Fulham’s defence remained resolute to the delight of the vast majority the 17,087 crowd.
After last week’s first leg, Jol admitted that the Cottagers struggled to cope with the Croatian side’s formation and especially use of wing-backs.
Split started with similar tactics again but Fulham began brightly and almost scored within two minutes when Murphy’s low free-kick was met by Damien Duff.
Fulham’s dominance of the opening exchanges continued as they searched for the opener, with the returning Clint Dempsey looking particularly dangerous.
It did not take long for the home side’s pressure to pay dividend as Johnson lost his marker to head home Duff’s inswinging corner in the 19th minute.
Split looked notably disheartened after falling behind and losing a couple of calls to Jol’s side, who continued to pen the visitors in their own half.
The pressure almost forced a second goal as Johnson turned provider for Dempsey in the 28th minute.
The 30-year-old striker chased down a seemingly lost ball and cut back for the American, who jinked past a couple of defenders before curling a shot just wide from the edge of the box.
Fulham continued to press and Johnson saw an effort blocked a couple of minutes later, before Murphy burst through and unleashed a low shot that forced goalkeeper Andrija Vukovic into a good save.
After the break, Split looked rejuvenated and came close to equalising through Vitaic’s stunning 30-yard free-kick, which dipped over the wall and just wide.
Ivan Katalinic’s side continued to press forward in numbers in search of an all-important away goal but a rash challenge by Velimir Vidic seemingly ended the tie.
The Bosnian defender scythed down Johnson as he cut into the box and skipper Murphy tucked away the resulting penalty in the 57th minute.
Johnson thought he had extended the Cottagers’ further a minute later after rounding keeper Vukovic to net – but the striker was adjudged offside and then received a yellow card for his remonstrations.
While Fulham looked dangerous on the attack, Split were still looking to net at the other end and Goran Milovic was unfortunate to see a close-range shot ricochet off the bar after connecting Ante Erceg’s free-kick.
Shortly after Fulham keeper Mark Schwarzer was forced to save low to his right after Oblinovic struck a 25-yard drive that threaten to bobble in.
Jol brought on Matthew Briggs and Mousa Dembele in a bid to freshen things up, but Predrag Simic soon found space to turn and launch a shot that Schwarzer did well to palm away.
Substitute Marko Jordan put a header wide in the closing stages, which was punctuated by bad challenges.
Fulham duo Murphy and Briggs received yellow cards in quick succession, before Split’s Damir Rasic was handed the same punishment.
The game ended on a lighter note, though, as newboy Pajtim Kasami came close to netting on his home debut with a lovely curling free-kick, which arced just wide just a minute after coming on..