World number 88 Petkovic was the better player in the biggest points, breaking the twice Grand Slam champion three times and committing 15 fewer unforced errors on a sun-soaked Louis Armstrong Stadium court.
Naomi Osaka was given a testing workout by Anna Blinkova as she began the defence of her US Open title, while Wimbledon champion Simona Halep snapped a string of early US Open exits with a 6-3 3-6 6-2 victory over Nicole Gibbs to reach the second round.
Simona Halep is living the dream after her Wimbledon triumph and the Romanian heads into next week's U.S. Open hoping for a new dawn at the season's final Grand Slam after early exits in the last two years.
No matter who wins the title decider on Centre Court, the one thing for certain is that it will be a historic occasion. The 37-year-old Williams is chasing an eighth All England Club singles crown which would see her match Australian Margaret Court's all-time record of 24 major singles titles.
Simona Halep will channel her inner child when she begins her French Open title defense against Ajla Tomljanovic on Tuesday having vowed to enjoy herself in the absence of the stifling pressure of previous campaigns in Paris.
Simona Halep reached her fourth Madrid Open final with a 6-2, 7-6(2), 6-0 win over Belinda Bencic on Friday. The world number three will move back to the top of the WTA rankings with a win in Saturday's final against either Kiki Bertens or Sloane Stephens.
Jelena Ostapenko created history after defeating Simona Halep in straight sets and clinched her first French Open, also her first Grand Slam. The 20-year old came back after losing the first set 6-4 and went onto win the last two sets comprehensively 6-4, 6-3.