Sixth-ranked Davydenko, the top seed in Moscow, had little trouble against 53rd-ranked Serra in the opening set but was made to work harder in the second, finally breaking the Frenchman in the eleventh game.
Davydenko is looking for his third straight and fourth title overall in Moscow.
Earlier, Uzbek qualifier Denis Istomin upset sixth-seeded Michael Llodra of France 7-6 (2), 6-3 in only his second ATP Tour match.
The 121st-ranked Istomin broke decisively in the sixth game of the second set and will face French veteran Fabrice Santoro in the second round.
Eighth-seeded Janko Tipsarevic of Serbia rallied to beat Russian qualifier Alexandre Kudryavtsev 4-6, 6-3, 7-6 (6).
In the women's draw, 2004 U.S. Open champion Svetlana Kuznetsova beat Li Na of China 6-4, 7-5.
The fifth-seeded Kuznetsova broke early in each set. She led 4-1 in the second set and had two match points serving at 5-3, but Li fought back to level at 5-5.
However, the Russian broke next game and then served out the match on her fourth match point.
"I had a very tough first-round match,'' Kuznetsova said. "Li Na beat many serious opponents this season and to win in two sets - I think, it's not a bad start to the tourment.''
Kuznetsova, ranked No. 7, has lost all seven WTA finals this season.
The women's field at the Kremlin Cup contains seven of the world's top-10 players - including No. 1 Jelena Jankovic - but U.S. Open champion Serena Williams, last year's runner-up in Moscow, pulled out because of an ankle injury.
Sixth-seeded Venus Williams was scheduled to play Flavia Pennetta of Italy later Tuesday.
In all-Russian matches, seventh-seeded Vera Zvonareva ousted Maria Kirilenko 6-4, 6-4 and Ekaterina Makarova beat Elena Vesnina 7-6 (4), 7-6 (1).
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