The Croatian seeded 11th is billed to clash with Kevin Anderson, a South African who saw off Jürgen Meltzer of Austria, in the second round.
Argentinean Juan Monaco also fell to lowly rated Benoit Paire as the Frenchman won the first set tiebreak 7-4, but Monaco recovered to take the second 6-1 but went down 6-4 in the final set.
Czech Radek Stepanek also suffered a three-set defeat to Italian Potito Starace. Helped by local support, Starace won 6-4, 4-6, 6-4 to set up a second round meeting with Roger Federer.
Second seed Federer who arrived earlier due to his early exit by Kei Nishirkori in the Madrid Open last week, said he has been practising and he is motivated and hungry to play some fine tennis again.
The Swiss will be starting fresh on Tuesday after the extra time he got to prepare.
“I arrived much earlier because of second round loss in Madrid,” Federer said. “I have been practising well, my body is well, really hungry and motivated to play again. I hope I can play a good tournament here.”
Andy Murray also had a first round bye and will face Spaniard Marcel Granollers who beat Nioklai Davydenko 6-3, 6-4.
The third seed from Britain said the Rome schedule would suit him better than Madrid where he was eliminated in the quarter-finals by Czech Tomas Berdych.
Men’s top seed Novak Djokovic will hope to make up for an early defeat also in Madrid when he begins in the second round on Tuesday against either Spain’s Albert Montanes or Slovakian Martin Klizan.
Rafael Nadal, winner of four clay court titles already this season after returning from injury, will begin with an Italian opponent in round two, either Fabio Fognini or Andreas Seppi.