"I was hoping it would not be the last time," said Clijsters, who plans to retire at the end of the season. "I'm so happy I can continue tomorrow."
Clijsters needed barely 15 minutes to take a 5-0 lead before a crowd of 10,500 at the Sports Palace.The 19-year-old Ivanovic lost the first set after two unforced errors.
"I was very close to my best level. Only my serve could have been better," Clijsters said, who won the title in 2004.
Mauresmo allowed the 11th-ranked Safina only four games after struggling in her opening match on Thursday.
"I am starting to play better and better," Mauresmo said. "So many things fit together now."
She will play Anna Chakvetadze on Saturday after the seventh-seeded Russian upset third-seeded Nadia Petrova 6-3, 6-4. If Mauresmo wins her next two matches, she will claim the jewel-encrusted trophy, which goes to the first player to win the tournament three times in a five-year span.
"It will be good to get to the final and then we will see," the third-ranked Mauresmo said. "The opposition is of such quality that I cannot look beyond that."
The Frenchwoman was in trouble Thursday and needed two long sets to beat 85th-ranked Virginie Razzano 7-6 (6), 7-5.
The 19-year-old Chakvetadze is chasing her second tournament win of the year after capturing the Hobart International in January. Last week, Mauresmo beat the Russian in two close sets at the Gaz de France in Paris.