The 2003 winner, bidding to reach her fourth successive grand slam final, won a hard-fought contest to set up a clash with Serbian 19th seed Jelena Jankovic.
"Lindsay played a great match," Henin-Hardenne said.
"She played an unbelievable level. I had to raise my level and be at my top to win today. I knew I could lose if I was just a little bit under this level. So she did push me a lot. It's been a very good test for me."
A break in the seventh game was enough to give the Belgian the first set but she then had treatment for a rib problem.
Davenport broke on her way to a 3-1 lead in the second set but Henin-Hardenne wiped out the advantage immediately and broke again in the ninth game to clinch her seventh consecutive victory over the American.
Henin-Hardenne, who said her rib injury would be fine by Friday, was expecting a tough outing against Jankovic.
"I am going to have a tough match I think, even if it looks maybe easy on paper when you look at the rankings," the Belgian said.
"On the court it's a totally different story. Jankovic is playing great tennis this week. It's going to be a tough, tough one for me."
After missing five months of the year with a back problem, Davenport was satisfied with her run at the Open.
"I'm not trying to pat myself on the back but I should have lost in the third round, was down two match points," she said.
"I wasn't feeling good when the tournament started. Got better. If you had told me that two weeks ago, if you had told me that two months ago, I would have been happy with that."
At the age of 30, Davenport she said she was unsure if she would play another U.S. Open.
"I have no idea," she said. "Twelve months is obviously a long time away but at this point I have no idea."
Davenport said Henin-Hardenne, who won the French Open and lost in the final of the Australian Open and Wimbledon, would be tough to beat.
"She hits the ball great. I think she competes well. She's a great athlete. In my mind, she's probably the best player in the world," she said.
