After battling through the qualifying draw, Bondarenko - one of a growing crop of mothers on tour these days - came out firing against Williams, breaking three times to take the first set and then pulling away in the second set, eventually getting to within a game of a routine victory going ahead 6-4, 5-2.
Williams came roaring back with four games in a row of her own and served for the second set at 6-5, even going up 15-0 in that game, but that's when the Ukrainian qualifier found her range again, winning 11 of the last 15 points of the match to close the No.1-seeded American out in straights, 6-4, 7-6(4).
"I gave my best efforts today," Williams said after the match. "Your first match is never perfect. She's played matches in the qualications and just never missed today, making great shots all game long.
"I'm really sad. I came here to play and to win but I ran into an opponent that was just too hot today. On a day like today I'm upset - it's normal, it's human. I calm myself down and focus and come back.
"That moment is that moment. We move on."
Bondarenko's win over the World No.15 is the 14th Top 20 win of her career, and most significantly the first since she returned to the tour just over a year ago. The best win of her career came against Williams, too - she beat the American when she was ranked No.3 in the world at Toronto in 2009.
"It was a hard match and it was my first on hardcourts since the grass season," Jankovic said after the match. "I had problems with my timing, the ball was light and really flying. I tried to come back but just couldn't do it today - my opponent was just so solid, and I just made too many unforced errors."
The other three seeds in action all advanced, with No.4 seed Alizé Cornet beating Yanina Wickmayer, 6-3, 7-5, No.5 seed Camila Giorgi battling two hours and 53 minutes to beat Dominika Cibulkova, 7-5, 5-7, 7-6(4), and No.8 seed Tsvetana Pironkova saving two match points down 6-5 in the third set to squeak past Russian qualifier Margarita Gasparyan in two hours and 42 minutes, 0-6, 7-6(4), 7-6(3).
? Daniela Hantuchová (@dhantuchova) July 21, 2015