Safin, a two-time Grand Slam champion, had to play five sets before beating Richard Gasquet, 7-6 (7-4), 4-6, 6-3, 6-7.
"I'm really happy with the way I played, definitely my best since Melbourne last year," said Safin, who has struggled through injury woes in the past two years, including his back, which caused him to miss a WTA tournament in Miami recently.
Davydenko, who is No. 6 in the latest world rankings, topped Arnaud Clement, 3-6, 6-2, 6-4, 7-6 (7-4).
Russia can put the tie on ice in Saturday's doubles, when the team of Dmitry Tursunov and Mikhail Youzhny faces Clement and Michael Llodra. The Russia-France winner will meet either the United States or Chile in September's semifinals.