The three-time French Open singles champion will now play Australia's Ashleigh Barty in the next round.
Williams has struggled on the return of serve in both of her matches here and she never got close to the Barty serve in the first set, winning just five points. "Still, there's no escaping the fear, the fear that I might not come back as strong as I was".
While trying to surpass Margaret Court's record of 24 Grand Slam titles might be one of the reasons she pushed herself to get back on court despite all her complications in childbirth, she also wants to see if she recover her pre-pregnancy form.
"I lost the first set and just thought "you know what?" And I don't want to get there.
A set and a break down, it looked like Williams' comeback slam following her maternity break would end in defeat by the 17th seeded Australian. She had played only four matches - going 2-2 - all season until this week.
Goerges will do well, however, to take note of what Barty said after the game: "Her level when it's not quite at her best is still pretty bloody good".
Serena Williams has spoken about coping with postpartum depression following her daughter's hard birth.
In Harper's Bazaar UK's July issue, the cover star bravely discussed her battle with postpartum depression following daughter Alexis Olympia's birth in September 2017. So I was just winging it in the last minute.
"Honestly, sometimes I think I still have to deal with it", she explained. I feel like everything else will fall into place, and it has. She then retired hurt during her semifinal with Anastasia Pavlyuchenkova in Strasbourg.
"I feel like a warrior in it, like a warrior princess kind of, queen from Wakanda maybe", she said smiling, following her opening round victory over Kristyna Pliskova at the French Open on Tuesday.
Williams suddenly found her groove and broke again to move into a 4-1 lead.
When on-target, her strokes are among the best in the game.
The singles victor between Barty and Williams will play either German 12th seed Julia Goerges or Belgian Alison Van Uytvanck on Saturday for a place in the last 16.