After last week's loss to sister Venus in the Montreal seni-finals, Williams faced another familiar foe in Stosur, who had beaten her in straight sets in the 2011 US Open final.
Williams has won all four meetings against the Australian since but the 17-times Grand Slam winner was made to work much harder on the Cincinnati hard courts than she did in Montreal last week where she pounded Stosur 6-0 6-2.
In a tight contest that did not feature a single break by either player, Williams needed nearly two hours to advance to the last 16.
"She was up in both of the (tie) breakers, I think it was just a great match, to be honest," said Williams, who has won 61 career titles but has never lifted the Cincinnati trophy.
"She served unbelievable, and I was like, I can't lose serve because she's just serving great.
"It was really intense."
Fourth seeded Pole Agnieszka Radwanska, fresh from her Rogers Cup win in Montreal on Sunday, cruised to a 6-2 6-2 win over Japan's Kurumi Nara, while German sixth seed Angelique Kerber beat Russia's Ekaterina Makarova 6-4 6-1.
Playing in her first event since successfully defending her Baku title last month, the 19-year-old served for the match at 5-4 and 6-5 but could not close it out and third seeded Czech Kvitova forced a tiebreak.
Svitolina held her nerve, however, and reeled off five straight points from 2-2 to clinch the upset and advance to the third round in her Cincinnati debut.
"I have to say number one I'm disappointed how I played today, for sure," said Kvitova.
"From the beginning I didn't feel very comfortable out there and I was trying to really fight. I just wasn't able to do that today. I'm not pretty sure why."
Canadian Eugenie Bouchard, seeded seventh, was ousted by Svetlana Kuznetsova, the Russian winning 6-4 3-6 6-2 to make it two from two in her career against Bouchard.
Bouchard, the Wimbledon runner up, has now been knocked out in successive tournament openers as the US Open draws closer.
Ivanovic easily took out American wild card Christina McHale 6-4 6-0 while Jankovic was too good for German qualifier Annika Beck 6-1 7-6(0).
Cincinnati Open results
Svetlana Kuznetsova (Russia) beat 7-Eugenie Bouchard (Canada) 6-4 3-6 6-2
8-Jelena Jankovic (Serbia) beat Annika Beck (Germany) 6-1 7-6(0)
9-Ana Ivanovic (Serbia) beat Christina Mchale (U.S.) 6-4 6-0
13-Flavia Pennetta (Italy) beat Taylor Townsend (U.S.) 6-4 6-3
4-Agnieszka Radwanska (Poland) beat Kurumi Nara (Japan) 6-2 6-2
16-Lucie Safarova (Czech Republic) beat Zarina Diyas (Kazakhstan) 6-4 6-2
Sabine Lisicki (Germany) beat 14-Sara Errani (Italy) 6-4 2-6 7-6(2)
1-Serena Williams (U.S.) beat Samantha Stosur (Australia) 7-6(7) 7-6(7)
Sloane Stephens (U.S.) beat Barbora Zahlavova Strycova (Czech Republic) 7-5 6-1
Anastasia Pavlyuchenkova (Russia) beat Karin Knapp (Italy) 6-1 6-3
Elina Svitolina (Ukraine) beat 3-Petra Kvitova (Czech Republic) 6-2 7-6(2)
6-Angelique Kerber (Germany) beat Ekaterina Makarova (Russia) 6-4 6-1
- Sports & Recreation
- Ekaterina Makarova
- Petra Kvitova
- Agnieszka Radwanska
- Angelique Kerber
- Elina Svitolina