Jankovic, playing her first match of the tournament after a first-round bye, coasted to a 6-2, 6-1 win over Italy's Flavia Pennetta.
Russia's Nadia Petrova defeated Ivanovic 6-1, 1-6, 6-2 in the tournament's first major upset.
Second-ranked Jankovic played up to her billing. If she wins this tournament, the Serb would return to No. 1 in the WTA rankings, replacing Serena Williams.
"It's a goal of mine to return to the top spot,'' Jankovic said. "You can go back and forth between the top three spots, but it's always nice to finish at No. 1.''
Jankovic will face Svetlana Kuznetsova in Friday's quarterfinals. The fifth-seeded Russian defeated Japan's Ayumi Morita 6-1, 6-1.
Third-ranked Ivanovic was also playing in her first match here and looked sluggish against Petrova, currently 20th in the rankings.
"I tried to dominate but I was making too many mistakes,'' Ivanovic said. "I played better in the second set but she served well in the third and was able to play at her pace.''
Petrova next plays sixth-seeded Agnieszka Radwanksa of Poland who defeated France's Marion Bartoli 6-2, 6-3.
Olympic gold medalist Elena Dementieva of Russia defeated France's Alize Cornet 6-0, 6-3 to reach the quarterfinals.
Dementieva, who won this tournament in 2006, will next face Slovenia's Katarina Srebotnik, who defeated Italy's Francesca Schiavone 6-4, 6-3.
Kaia Kanepi of Estonia defeated Virginie Razzano of France, 6-4, 6-2 to set up a quarterfinal match with fourth-seeded Dinara Safina of Russia.
Jankovic advances to Pan Pacific Open quarters
Russia’s Kuznetsova advances at Pan Pacific
Pablo Remaining Positive
