Djokovic must also be lined up in doubles, alongside Nikola Cacic, against the world's best pair Nikola Mektic and Mate Pavic, notably Wimbledon winners and crowned Olympic champions in 2021.
Mektic and Pavic have so far won the three doubles they have played since the start of the competition.
Against Cilic, ex-world No. 3 today 30th, Djokovic accelerated from 4 games throughout the first set.
The Serb then left only two games to his Croatian opponent.
Cilic got himself eight break points in total, but he did not convert any.
Previously, Borna Gojo, 279th in the world, brought Croatia the first point by signing a new feat, this time against Dusan Lajovic (33rd), beaten 4-6, 6-3, 6-2.
Before the Davis Cup, Gojo (23) had only one victory over a top 100 player. He is now four.
In the quarter-finals already, he had offered the 27th world, the Italian Lorenzo Sonego.
Before that, he won against the 61st in the world, the Australian Alexei Popyrin.
The second semi-final will pit Daniil Medvedev's Russia against Germany on Saturday afternoon (from 1:00 p.m.).
The final is scheduled for Sunday.
© 2021 AFP