Williams was broken in the first game of the match, after being down 0-40 at one point.
The American lost the next game - to love - as Parmentier found her serving range early.
However, to the obvious delight of the near sell-out crowd, Williams eventually kicked into gear.
From 3-1 down, the 35-year-old won five successive games to take the set, mixing up vicious serves and returns with some silky drop shots.
Williams broke early in the second set - and looked to be on the downhill slope to the finish - but Parmentier showed impressive resistance. She broke back midway through the set, as Williams looked for guidance from her coach sat courtside.
Williams fended off three break points in the crucial sixth game - unleashing a booming cross court winner to hold for 3-3 and then broke Parmentier in the next game.
The 22-time grand slam winner had to fight until the end, saving two break point opportunities in her next service game, but eventually prevailed in 76 minutes.