Fifth-seeded Cilic converted only three out of 10 break points, two of them Lajovic double-faults.
Cilic improved to a 16-1 record in his last five attempts here, winning titles in 2009, 2010 and 2013.
"I served very well," Cilic said, adding "some things did not work well today and I made a bit too many unforced errors."
Sela led by a set and 5-3 before Rosol broke back and forced a tiebreaker. But Sela moved into an early lead again and closed out the match.
Russian qualifier Andrey Kuznetsov beat 2008 champion Sergiy Stakhovsky of Ukraine 6-4, 7-6 (8) for his first tour win since July, while Andrey Golubev of Kazakhstan defeated Victor Hanescu from Romania, 7-6 (6), 4-6, 7-6 (5).