The Serb, seeded 11th in Tokyo, beat Andrea Hlavackova 6-3 2-0 to advance after the Czech retired with a thigh injury after just 44 minutes.
"That's the only reason I'm still here," Ivanovic, who climbed to the top of the women's rankings after winning the 2008 French Open, told Reuters.
"I already achieved two of my biggest dreams in winning a grand slam and being number one in the world.
"But I believe I can still be at the top level and winning grand slams. Otherwise I wouldn't be here," added the 24-year-old, the winner of 11 WTA Tour titles.
Nine of the world's top 10 women are competing this week at the Tokyo event, with the top eight seeds receiving byes into the second round.
The Serb who reached the US Open quarter-finals earlier this month, faces Urszula Radwanska in the second round after the Pole beat Japan's Kurumi Nara 6-2 6-4 .
Former world number one Caroline Wozniacki squeezed through to the second round just one day after ending a 13-month title drought in South Korea.
The Dane made hard work of beating Serb qualifier Bojana Jovanovski 6-0 3-6 6-4 in a match halted for an hour in the third set by lightning flashes and torrential rain.
Wozniacki, who captured the Korea Open on Sunday, powered through a first set played in a warm breeze before fatigue hit her in the second.
The heavens broke at 3-3 in the decider and Wozniacki, down 15-30, eventually dropped her serve after waiting for the roof to be closed and the waterlogged court to be mopped dry.
Normal service was quickly resumed, however, as the 10th seed took the next three games to wrap up victory in two hours 17 minutes after forcing Jovanovski into a wild backhand.
"I was very lucky the rain came at 3-3 in the third," Wozniacki said. "I was feeling tired and it gave me a little time to relax and get my body back together."
France's Marion Bartoli bundled out Japan's Kimiko Date-Krumm 6-1 6-4, just four days before the local favourite's 42nd birthday.
Wildcard Date-Krumm, who won the title in 1995, left the court fuming at a boisterous fan, glaring back at the seats as she walked to the net to shake hands with ninth seed Bartoli.
"I was told there was a drunk fan," said Date-Krumm, who shouted angrily in the direction of the spectator after netting a forehand during an attempted fight-back.
"It was a big game and a big point. You're focusing so hard and it's extremely disappointing when people who are meant to be supporting you are drunk and shouting when you hit the ball."
Italy's former French Open champion Francesca Schiavone squeezed past Yaroslava Shvedova of Kazakhstan 4-6 7-6 6-4 to set up a second round match with Australian Samantha Stosur.
Russia's Nadia Petrova overpowered China's Peng Shuai 6-1 6-4, ousting one of three Chinese taking part despite a fierce political row between China and Japan over disputed islands.
- Caroline Wozniacki