Jankovic and Bondarenko traded breaks of serve at the start of the match but once Jankovic broke for a 3-2 lead, she never lost another game.
The Serb was assured of becoming No. 1 when the new ranking come out Monday after Serena Williams' loss to Li Na on Wednesday. Jankovic is looking for back-to-back titles after winning last week's China Open.
"I am pretty happy with the way I played, it was my first match indoors,'' said Jankovic, who lost the U.S. Open final to Serena Williams.
"It feels great to be back at No. 1 but my goal is to finish the year as No. 1,'' Jankovic said. "I'm playing better and better, I am improving. I don't feel any extra pressure, if anything then extra motivation.''
Serena's sister Venus, seeded sixth, served 12 aces to beat Kateryna Bondarenko, Alona's younger sister, 6-4, 6-2 and also advanced.
Williams dominated the Ukrainian qualifier and won in 66 minutes.
"I'd like to serve like that in every match,'' Williams said.
Williams, the Wimbledon champion, fell behind 3-1 but recovered to break serve twice in winning the first set.
"She played really well,'' Williams said. "She had an early break and I needed to break her back. I felt comfortable on the court.''
Third-seeded Dinara Safina rallied in the second set to beat qualifier Tsvetana Pironkova 6-1, 7-6 (6) to set up a quarterfinal clash with Williams.
Two other Russians also advanced to the last eight, Vera Zvonareva and Nadia Petrova.
Seventh-seeded Zvonareva spoiled Marion Bartoli's 24th birthday by beating the Frenchwoman 6-2, 6-0, while Petrova overcame Patty Schnyder of Switzerland 6-4, 6-1.
"I didn't give her a chance to get into the match,'' said Zvonareva, the Olympic bronze medalist. "I played pretty well and consistent.''
Zvonareva next plays Jankovic, who beat her at the China Open.
Petrova, the 2006 champion in Stuttgart, will meet Li in the quarterfinals.
Safina trailed 3-5 in the second set after having her serve broken but broke right back to love. She never trailed in the tiebreaker and used her second match point to close out the encounter.
Safina still has a chance at finishing the year at No. 1 after a breakthrough season during which she has won four titles. She was also runner-up at the French Open and the Olympics and a semifinalist at the U.S. Open.
"It wasn't an easy match, I didn't play at my best. I was going for my shots even if I was missing some,'' Safina said.
Jankovic already held the No. 1 spot for one week in August.
Since Justine Henin retired in May, four players have held the No.1 ranking: Ana Ivanovic, Jankovic, Maria Sharapova and Williams.
Ivanovic and Sharapova are the only top-10 players who did not come to Stuttgart.
Advocaat: We Can Beat Juve & Madrid
Venus advances at Porsche GP
