Johanna Larsson dropped just five games in a positive start on the clay in Croatia.
Andy Murray was in poor form before the French Open. "I came in playing garbage," said the Briton with a smile after reaching the semis.
A French Open victory over Simona Halep would see Karolina Pliskova start next week on top of the rankings.
World number one Andy Murray was not at his best on Wednesday, but said: "It's a huge step in the right direction for me."
Pre-tournament favourite Simona Halep thought "it's over" for her at the French Open before pulling off an astonishing fightback.
Kei Nishikori won the first set against Andy Murray, but the Japanese was guilty of too many errors thereafter against the world number one.
Marin Cilic has not beaten Stan Wawrinka for seven years and there was no danger of him ending that sequence in Paris.
Dominic Thiem's reward for seeing off Novak Djokovic is a semi-final clash with Rafael Nadal, who is taking nothing for granted.
A remarkable second-set turnaround paved the way for Simona Halep to reach the last four of the French Open on Wednesday.
Caroline Garcia's French Open run is over following a quarter-final defeat to Karolina Pliskova.