Agnieszka Radwanska, aged 17 and still in high school, embarrassed the Swiss 4-6 6-3 6-2 in a two-hour comeback. Hingis, titleholder in 1997 and 2000, produced 43 unforced errors and missed 14 of 20 break point chances.
"Before the match, I didn't believe I could beat her, because she's the favourite," the 49th-ranked Radwanska told reporters. "And a few years ago she was my favourite player."
Hingis said: "I just wasn't able to pull it off today. It's been like that the last three, four weeks. I'm getting tired of losing matches which I'm supposed to win.
"I need to recharge my whole body, and mostly my head."
Henin, seeded second, recovered from 1-5 down in the final set to defeat Virginie Razzano 6-2 2-6 7-6, with the Frenchwoman twice standing two points from an upset victory.
Belgium's fourth seed Clijsters continued her long goodbye to tennis with retirement looming later this year after her marriage, claiming a victory over Australian Samantha Stosur 6-4 6-2.
Men's second seed Rafael Nadal advanced to the fourth round after Belgian opponent Olivier Rochus withdrew with a foot injury before their evening match.
Two-time French Open winner Nadal is making his fourth straight appearance at the tournament with his best result coming in 2005 when he lost to Roger Federer in five sets.
Britain's Andy Murray stretched a run of form with an easy 6-3 6-1 win over lucky loser Robert Kendrick. The American entered the field when Lleyton Hewitt pulled out.
Pacific Life Open finalist Novak Djokovic of Serbia, seeded 10th, beat Michael Llodra of France 6-4 6-1.
