The seventh-seeded Serb, who last made the semi-finals of a major on her way to her only Grand Slam title in Paris in 2008, will face either Czech 13th seed Lucie Safarova or Garbine Muguruza, the 21st seed from Spain, for a place in Saturday’s final.
It will be Ivanovic’s fifth last-four appearance at a major following similar runs to the 2007 and 2008 semi-finals at Roland Garros, Wimbledon in 2007 and the Australian Open in 2008.
“I don’t know whether to feel happy or old,” said the 27-year-old, who has now won all her seven meetings against Svitolina, seven years her junior.
“It was very tough to play today. The wind was really strong and the ball was bouncing all over the place so I just needed to stay calm and use my feet more.”
Ivanovic and Svitolina, who was bidding to become the first Ukrainian woman to reach the semi-finals of a Grand Slam, exchanged breaks in the second and third games of the opening set.
But the vastly more experienced Serbian, watched from the stands by German World Cup-winning boyfriend Bastian Schweinsteiger, broke again for 3-1 to lay the foundation for clinching the first set.
Breaks in the first and seventh games of the second helped Ivanovic into a comfortable 5-2 lead and despite double-faulting on her second match point, she sealed victory on her third with a sweeping forehand winner.
Ivanovic was rewarded for her positive approach on Court Philippe Chatrier, her 37 winners to just eight for Svitolina telling its own tale.