Davydenko has not been able to add to his 10 career ATP titles and has yet to reach a final in 2007.
But the world number four continues his trademark nonstop scheduling, playing in China just over 48 hours after losing a US Open semi-final to Roger Federer.
The Russian has made semi-final runs at Roland Garros and Flushing Meadows this season.
Davydenko is hoping to improve upon his quarter-final in his Beijing debut a year ago. But he was more than a match for Fleishman, who earned his first career quarter-final at Los Angeles, where he beat Fernando Gonzalez.
Croatian fourth seed Ivan Ljubicic and number five defending champion Marcos Baghdatis also advanced in the first round.
Ljubicic defeated Japan's Kei Nishikori 6-3, 6-4 while Baghdatis stopped Shao-Xuan Zeng of China 7-6 (7-3), 7-5.
Seventh-seeded Frenchman Jo-Wilfred Tsonga advanced over Rohan Bopanna 6-3, 1-0 when the Indian had to quit their match.
Two Serbs advanced, with Boris Pashanski beating Yen-Hsun Lu of Taiwan, 6-7 (4-7), 6-2, 7-6 (8-6) and Viktor Troicki accounting for Russian Teimuraz Gabashvili after losing the opening set.
German fortunes were mixed. 2000 Hong Kong champion Nicolas Kiefer beat Israeli Dudi Sela 6-2, 6-3 while Croatian teen Marin Cilic stopped veteran Rainer Schuettler 6-7 (5-7), 6-3, 6-3.
Davydenko is playing with the distraction of match-fix suspicions after a loss he suffered in July which has sparked a probe by the ATP and Scotland Yard investigators.
The Russian, who will need all of his concentration over the next few weeks for both Beijing as well as a Davis Cup semi-final in Moscow against Germany, is trying to shake off his potential crisis of confidence.
"I just concentrate on my game, I want to earn some points for Shanghai (November's Masters Cup). I want to stay in the Top five this year and maybe go better.
"I don't care what's happening out there, for me it's more important what I do right here and now."