There were no breaks in the first eight games of the match, but the No.11-seeded Ivanovic broke at 4-all and completely broke the match open, eventually cruising to a straight set victory, 6-4, 6-2.
Ivanovic finished with a phenomenal crosscourt forehand winner, her 22nd winner of the match - outnumbering 21 unforced errors. Jovanovski was in the negatives, 15 winners to 26 unforced errors.
Jovanovski couldn't break through on the Ivanovic serve either - she was zero for six on break points.
"It's always strange playing someone from your own country, and actually we'd never played before, though we have practiced a lot and played Fed Cup together," Ivanovic said of Jovanovski. "It was a tough match today, especially in the first set, but I'm happy I was able to get through this one."
This is the fastest Ivanovic has reached 25 match wins on a season in her career. Before this year the earliest she got to 25 was at the French Open - in 2007 she got to 25 in the second round there (by beating Sania Mirza) and in 2008 she did it in the quarterfinals there (by beating Patty Schnyder).
Ivanovic is also just the third player to reach 25 this year, with Carla Suárez Navarro currently at 27 and Agnieszka Radwanska at 25 as well. Both of those players will try to add to those totals on Wednesday, and Jelena Jankovic will try to join the club as she goes for her 25th on Wednesday too.
Earlier, three of the favorites for the title moved through to the third round as well, with No.2 seed Li Na winning an all-Chinese battle against Zheng Jie, 6-2, 6-3, No.5 seed Petra Kvitova recovering after a disastrous first set to beat Varvara Lepchenko, 2-6, 6-2, 6-1, and No.8 seed Maria Sharapova rallying from 4-1 down in the third set to win an absolute grinder against Christina McHale, 6-1, 4-6, 6-4.
McHale was five points from victory leading 4-2, 40-30 in that third set, but Sharapova hung tough.
"After a really good start to the match, I didn't keep that level," Sharapova said. "I didn't keep doing what I was doing. I think I had a bit of a letdown. But she's a good competitor - she won't just give matches away, and she works really hard out there, and I think she really showed that today."
Next up for Sharapova is Sam Stosur, who won a see-saw battle with Garbine Muguruza, 7-5, 3-6, 6-1.
Sharapova leads Stosur in their head-to-head, 12-2, though that started as 9-0 and has tightened up.
Other winners were No.10 seed Sara Errani, who beat fellow Italian Francesca Schiavone, 6-3, 6-1, No.16 seed Sloane Stephens, who avenged a loss in Doha against Petra Cetkovska with a 6-4, 2-6, 6-3 win over the Czech qualifier, and Lucie Safarova, who routed Magdalena Rybarikova, 6-1, 6-2.