Croatia looked more energetic at the start of the second spell and almost took the lead in the match in the 51st minute but Milan Badelj's rocket from outside the box crashed against the crossbar.
Perisic, with Luka Modric the only player not rested, struck in the last minute to set up a round-of-16 game against Denmark after Milan Badelj's second-half goal was cancelled out by Gylfi Sigurdsson's penalty.
Iceland still has a chance of reaching the Round of 16 as the runner up in Group D. They are two points behind second-place Nigeria, so they must beat Croatia to have any shot of progressing.
Croatia claimed top spot in Group D of the 2018 World Cup in Russian Federation courtesy of a 2-1 win over tournament debutants Iceland at the Rostov Arena this evening.
Shortly after half-time though, Milan Badelj put Croatia in front with a textbook half-volley from Perisic's cross.
Regardless of the late drama in the first period, it was Croatia who came out on the front foot in the second period and Badelj might have opened the scoring when he saw his effort from range deflected onto the crossbar with Hannes Thor Halldorsson beaten.
Croatia started with plenty of possession as Iceland sat back in the opening moments and Perisic might have headed home from a corner, only to be stifled by some smart defending from both Sverrir Ingi Ingason and Ragnar Sigurdsson.
Iceland made three changes from their defeat to Nigeria, with Johann Gudmundsson the most notable change back in midfield, replacing Rurik Gislason.
They threw everything forward but to no avail.
Croatia kept its flawless record at the 2018 FIFA World Cup while sending Iceland home on Tuesday.
Heimir Hallgrimsson's men were pressurising the Croatians in the final five minutes as they went in search of another goal.
He was one of nine players drafted into the Croatia XI after Thursday's win against Argentina, but one wouldn't have suspected there were so many alterations based on the sustained quality of their play.
As a result, the first stanza ended goalless, although Iceland had the slight upper hand.
