Fifth seed Cilic needed just over 90 minutes to edge out fellow Croatian Dodig 7-5 6-4 in Zagreb, clinching his 18th win from his last 19 matches at the ATP World Tour tournament in the process.
Cilic told atpworldtour.com: "It was tough. There was a lot of emotion on the court. I was Ivan's best man at his wedding and we have been friends for many years.
"It was not easy to play. A few points decided the match."
The world number 37 will next tackle world number 358 Bjorn Phau after the German qualifier overcame Dudi Sela 6-4 6-3 while the other semi-final sees in-form British number two Evans pitted against top seed Tommy Haas.
Twenty-three-year-old Birmingham native Evans - a lucky-loser entrant thanks to Radek Stepanek's withdrawal - shocked many when ousting Jan Hajek and Michael Berrer in early rounds but went one better in the last eight, overcoming Philipp Kohlschreiber 6-4 2-6 6-4 to reach his first ever semi-final on the tour.
Evans can expect to rise to around number 124 in the ATP rankings and is the first British player, other than Andy Murray, to reach the last four of an ATP World Tour tournament since James Ward did so at the Aegon Championships in June 2011.
In the last quarter-final of the day, Haas - a quarter-finalist at last year's French Open - managed to keep Andrey Kuznetsov at arm's length and rode out a 7-6 (8-6) 6-4 victory.