Pennetta, seeded 12th in Paris, went down 5-7 6-4 6-2 to world number 99 Johanna Larsson, the Swede battling back from a set down to progress to the third round.
Meanwhile, 29th seed and seven-time grand-slam champion Williams, also suffered disappointment as, like Pennetta, she lost out moving one set to the good against Anna Schmiedlova, going down 2-6 6-3 6-4.
Pennetta and Larsson traded multiple breaks in the opening set, the Italian recovering from a break down at 4-5 to win the next three games and take the lead.
Larsson hit back in the second, claiming a crucial break in game nine to set up the opportunity to level the match, and then dominated the decider, surging into a 4-0 lead before holding out comfortably to shock her opponent.
The Swede will now face 18th seed Eugenie Bouchard, who came from a set down to beat Julia Goerges 2-6 6-2 6-1.
Joining them in the third round will be Schmiedlova, the world number 56 seeing off Williams.
Williams dominated the first set, reeling off five games from 2-1 down to move in front, but a double break midway through the second helped the Slovak level.
An early double break in the final set put Schmiedlova 3-0 up and although Williams clawed one break back, she could not repeat the feat as she failed to reach the third round for a third year in a row.