Both women reached the fourth round at Wimbledon, and both had not dropped a set all week in Switzerland, but Martic succeeded in beating Garica 6-4, 1-6, 6-3 for the first time in her career on Saturday.
Martic reached her first final since 2019, and she will meet Danilovic, who cruised to an upset victory over Anastasia Potapova earlier on Saturday.
Potapova, who is world No. 79, had been favoured to win heading into the match, but the tournament threw up yet another surprise as Danilovic won 6-3, 6-2.
Information from the Associated Press contributed to this report.