Davydenko held serve throughout in beating Daniel Koellerer of Austria 6-2, 6-3 before Flavio Cipolla of Italy upset Wawrinka 6-4, 6-1.
"The early matches of the new season are always tricky, irrespective of who you are playing against and where you'd finished last year,'' said Davydenko, who won three titles last year. "I was consistent, but can't say I'm not confident with the manner I played today.
"My service was OK, but I wasn't pleased with my baseline game and kept waiting for my opponent to make mistakes,'' the Russian added. "Winning matches and good results isn't the same thing. To me, a good result is the reflection of how I feel about my play.''
Davydenko will next face wild card Lukas Dlouhy of Czech Republic, who needed three sets to beat Go Soeda of Japan on Monday.
"It's the start of a new season with lots to discover,'' Davydenko said. "I just wish to play in the same manner, but with better baseline strokes.''
Cipolla, ranked 138th, said he benefited from playing in the qualifying tournament for his win over Wawrinka, who was returning to competitive tennis for the first time this season.
"Our only previous encounter was in the U.S. Open, where I lost a very tight match to him after leading by two sets,'' Cipolla said. "I was confident from the beginning and knew that I could beat him.
"With a good start to the season, I'm looking to soon improve my ranking to the first 100, and then hope to finish the year among the top 50,'' he said.
Fourth-seeded Ivo Karlovic of Croatia and two-time Chennai Open champion Carlos Moya of Spain also advanced to the second round. Karlovic recovered to beat Rajeev Ram of the United States 6-4, 6-3, while the sixth-seeded Moya overcame Danai Udomchoke of Thailand 6-3, 7-6 (4).
Moya, a former top-ranked player and the 1998 French Open champion, trailed in the second set before breaking Danai to level at 3-3.
"I'm usually a slow starter, but I got going quickly today,'' said Moya, who won the Chennai Open in 2004 and '05.
Also, seventh-seeded Janko Tipsarevic of Serbia beat Pablo Andujar of Spain 6-3, 6-2; Denis Istomin of Uzbekistan defeated Rohan Bopanna of India 6-4, 7-6 (3); Andreas Beck of Germany beat Roko Karanusic of Croatia 6-1, 6-0; Indian wild card Somdev Devvarman beat Kevin Kim of the United States 6-3, 6-3; and Ivo Minar of the Czech Republic eliminated Wayne Odesnik of the United States 6-3, 6-0.
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