Third-seeded Myskina, off to a lackluster start to the season after leading Russia to the Fed Cup championship in November, lost in the last eight in Dubai for the fourth straight year.
She swept the first-set tiebreaker against Schnyder, and rallied from 4-0 down to reach match point at 6-5 on the Swiss player's serve.
Schnyder saved it with a forehand winner and hit an overhead smash to keep her serve, and set up another tiebreak, which she won 7-2. In the third set, Schnyder broke Myskina in the sixth game, and the eighth to love to close the two-hour contest.
"It was a really tough match and I was lucky to save the match point," said Schnyder. "And I am looking forward to winning two more matches here."
Schnyder was in sight of her second title this season, but meets Davenport having won only two of eight previous matchups.
"She is a great competitor, one of the few pure lefties on the tour," Davenport said. "And she uses her advantage well, swinging the ball in. She plays the ball well on both sides and it should be an interesting match.
"I just have to serve well, be aggressive, hit the ball hard and not allow her to get into any rhythm," the American added.
Davenport edged ahead of Martinez 9-8 in their matchups since 1994.
Davenport breezed through the first set, breaking Martinez three times. But Martinez rebounded in the second set, going up 3-1. The American broke in the eighth game to level at 4-4, and broke again to win the match between the former Wimbledon winners.
"I made a few errors and allowed her to come back into the match, giving her confidence," Davenport said. "She broke me a few times but I still managed to come back, and I feel good about that."
Williams remained unbeaten in 2005 through 10 matches, racing to a 5-1 lead against Hantuchova.
But she dropped her serve in the eighth game, serving a double fault and netting a volley on the run at 30-40.
Hantuchova climb back to 4-5 but Williams served two of her six aces to finish the set.
In the second set, Williams showed some deft touches at the net to break in the third game, but double-faulted at 30-40 to lose the fourth.
However, an erratic Hantuchova lost her serve in the next game, and at 3-5 down netted a backhand to give Williams match point, which the American claimed with an overhead winner.
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