The former top-ranked Russian, who has been struggling since returning from a 10-month injury layoff, will face Iveta Benesova of the Czech Republic in the quarterfinals on Thursday. Benesova defeated Taiwan's Chang Kai-chan 7-5, 6-2.
Sharapova, 25th in the world rankings, took control of the match in the second set when she broke Kleybanova three times to open up a 5-0 lead. Kleybanova broke back in the sixth game and held before Sharapova served to win the set.
"She started off really strong," Sharapova said. "I was too slow in the beginning. Nobody had much of a warmup today, we kind of had to warm up in the first few games and she did a much better job of that than me."
Sharapova, who broke the unseeded Kleybanova three more times in the final set before closing out the match, won her first tournament as a professional at the Japan Open in 2003 and won in Tokyo in 2005. With the top six seeds all out of the tournament, she is positioned well for another shot at a title in the $2 million event at Ariake Colosseum.
"Some of the other girls not in the top 10 have played really well here," Sharapova said. "You've got to expect that from every player you play and focus on the task at hand."
Jankovic is the highest-seeded player left in the tournament but said she won't allow that to add to the pressure of winning here for the first time.
"I don't really think about that," Jankovic said. "I just think about my game and what I have to do on the court. I don't want to put too much pressure on myself."
The former world No. 1 will meet France's Marion Bartoli in the quarterfinals on Thursday. Fourteenth-seeded Bartoli recovered from a set down to defeat Anastasia Pavlyuchenkova of Russia, 4-6, 6-2, 7-5.
Jankovic has lost to Bartoli twice this year, at the Australian Open and at Stanford.