Hingis was facing Davenport for the first time since 2001
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Martina Hingis enjoyed the best win of her comeback as she saw off second seed Lindsay Davenport at the Pacific Life Open in Indian Wells on Tuesday.
The Swiss star has risen to 32 in the world rankings since returning to the game in January after three years out.
Hingis beat Maria Sharapova in Tokyo last month but a battling 6-3 1-6 6-2 win over Davenport was evidence that she continues to improve.
Sharapova and top seed Justine Henin-Hardenne later made progress.
Third seed Sharapova had a 7-6 (7-2) 6-1 win over Shahar Peer of Israel, while Henin-Hardenne beat Japan's Ai Sugiyama 6-2 6-1.
Hingis plays Dinara Safina next after her 6-1 6-3 win over Anastasia Myskina.
"When I saw the draw, I was looking potentially fourth round to play Lindsay," said Hingis.
"She's the one you kind of aim for, you've been playing all these years. You definitely find out where you're at and what your potential is.
"I'm over this bump now. I'm just looking forward to the next match because as soon as you start looking too far ahead, you might lose focus."
Davenport, who has been struggling with a back injury, said: "I still feel like I would have beaten a lot of players today. She's going to be at the top as soon as she plays more and more.
"It's just a matter of her getting more tournaments under her belt."
Elsewhere, fourth seed Elena Dementieva cruised past China's Li Na 6-3 6-2, and eighth seed Ana Ivanovic beat Anna Chakvetadze 6-3 6-3.