Hingis, the top seed, had little trouble defeating Russia's Nadejda Petrova 6-1 6-3, although Hingis trailed 1-3 in the second set.
Ninth-seed Amanda Coetzer of the United States was the ony seed to fall on Wednesday when Magdalena Maleeva of Bulgaria scored a 6-3 6-2 victory.
Davenport, surprised by the aggression and precision of Henin's groundstrokes, lost her serve twice to drop the first set 6-3 in 34 minutes.
In the second Davenport, seeded second, was treated for a slight foot injury and went on to save four break points before getting to a tie-breaker. Then, serving and returning better, she imposed her powerful game to capture it by 7-3 and breezed through the final set.
``My real mistake is that I didn't believe in my chances to win that match before stepping onto the court,'' Henin said. ``If I did, I probably would have broken her in the second set, and I would have played the tie-breaker in a more aggressive fashion.''
Henin came close to upsetting Davenport the only previous time the two had met, at the 1999 French Open.
Henin who was sidelined for six month due to injuries is finally back to the WTA Tour in full health.
``I thought she played unbelievable in the first set and a half and I was a bit slow to react to the changing conditions from being in California for five weeks or so,'' said Davenport who lost the final in Manhattan Beach on Sunday to Serena Williams.
Winner of the Manhattan Beach event for the second consecutive year, Williams is continuing her string of victories as she crushed Switzerland's Patty Schnyder 6-1 6-2 in just 47 minutes.
``Even if she sometimes makes mistakes, you feel there is nothing you can do because you know that she can raise the level of her game whenever she needs to,'' Schnyder said.
In the round of 16, Serena will meet Anna Kournikova, seeded 11th, who defeated Sabine Appelmans of Belgium.