Roma won the first leg by just one goal in Stadio Olimpico, but Fabio Capello made a number of changes to his team - including playing French full back Vincent Candela up-front.
The home side took advantage of the weakend Roma team and went ahead after 33 minutes through Nino Bule - who turned in Peter Krpan's cross.
Roma looked like they would be dragged into extra time by the Croats, but it was not to be for the home side.
With just five minutes remaining keeper Zlatko Runje came to close the ball down, but he slipped and allowed the ball to run past him - which left Cassano with the simple task of tapping home.
Capello will not have been happy with the performance, but his side are through and that is what counts.
An impressive Parma cruised into the third round of the Uefa Cup with a 5-0 win over Salzburg at The Ennio Tardini.
The Serie A outfit had already won the first leg 4-0 and now they record an even bigger margin of victory in the return.
Two goals in the first seven minutes from Benito Carbone set Parma on their way and Emanuele Filippini (pictured) made it 3-0 just before the interval.
Youngster Antonio Sorrentino (47 & 81) grabbed two in the second half to seal victory.
Perugia moved into the next round after a 1-1 draw against Greek outfit Aris Saloniki gave them a 3-1 aggregate win.
Massimo Margiotta gave the Italians the lead after 27 minutes.
Nikos Papadopoulos curled home a free kick in the final minute, but it was too little too late for the hosts.
Aris Saloniki 1-1 Perugia (1-3 agg)
Hajduk Split 1-1 Roma (1-2 agg)
Parma 5-0 Salzburg (9-0 agg)
