Cilic, the top seed for the tournament, has won four of his eight ATP championships in Croatia, including taking the Zagreb event in 2009 and '10. He advanced to this year's quarterfinals with a 6-2, 6-3 decision over Zemlja.
Cilic had 11 aces and didn't drop his serve, winning three-quarters of the points when serving. He finished off three of his four break opportunities.
Ivan Dodig edged by Ivo Karlovic 7-6 (7-2), 6-7 (2-7), 6-3 in an all-Croatian match. Dodig managed just two break changes against the hard-serving Karlovic, including a break at love in the sixth game of the third set.
The tournament lost three seeded players, including No. 2 Andreas Seppi, who withdrew before Thursday's play. Robin Haase knocked off fifth-seeded Martin Klizan 6-2, 4-6, 6-4 and Blaz Kavcic ousted No. 6-seeded Marcos Baghdatis 3-6, 7-6 (7-2), 6-4 in second-round upsets.
Fourth-seeded Jurgen Melzer gained the quarterfinals with a 1-6, 7-6 (7-5), 6-2 win over Somdev Devvarman while Lukas Rosol got by Flavio Cipolla 6-4, 2-6, 6-3 and Philipp Petzschner beat Dino Marcan, inserted in Seppi's slot in the draw, 6-3, 6-4.
Cilic faces Kavcic and No. 3-seeded Mikhail Youzhny goes against Dodig in the draw's top-half quarterfinals. The other matches Friday have Melzer playing Rosol and Haase meeting Petzschner.