Jancovic, 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, currently 20th in the rankings, defeated Ivanovic 6-1, 1-6, 6-2 in the tournament's first major upset.
Jankovic, No. 2 in the world, played up to her billing. If she wins this tournament, the Serb would return to No. 1 in the WTA rankings, replacing Serena Williams in the top spot.
"It's a goal of mine to return to the top spot,'' said Jankovic. "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 quarterfinal. The fifth-seeded Russian defeated Japan's Ayumi Morita 6-1, 6-1.
Ivanovic, who is third in the world rankings, was also playing in her first match here and looked sluggish against Petrova.
"I tried to dominate but I was making too many mistakes,'' said Ivanovic. "I played better in the second set but she served well in the third and was able to play at her pace.''
In an earlier match, 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 the winner of Thursday's later second-round match between Slovenia's Katarina Srebotnik and Francesca Schiavone of Italy.
Sixth-seeded Agnieszka Radwanksa of Poland defeated France's Marion Bartoli 6-2, 6-3 and will face Petrova in the quarterfinals.
Jankovic advances at Pan Pacific Open
Pablo Remaining Positive
Russia’s Kuznetsova advances at Pan Pacific
