It was Davenport's first outing since she was beaten by Serena Williams in last Saturday's Australian Open final in Melbourne.
Sydney Olympic silver medallist Dementieva, seeded four, shrugged off a shaky start that saw her hit four double faults to trail 0-2 before scoring a lopsided 6-2, 6-2 win in 63 minutes.
"I lost the first two games and then I won it 6-2, six games in a row. I usually have a slow start," said Dementieva, runner-up at Roland Garros and the US Open last season.
"But I was very comfortable on the court, because I knew that I just have to find my rhythm and I can win this match, so I think I played very well today, even though I lost my game from the beginning," she added.
Dementieva said the experience of reaching the finals in the Grand Slams last season had helped her beat better players, but said there was room for improvement.
"Especially my serve, but for the moment I know must continue to work hard and I feel like if I do, I can do it (winning a Grand Slam) this year," added the 23-year-old Russian.
Japan's number two Shinobu Asagoe kept local hopes alive when last year's US Open quarter-finalist whipped Roberta Vinci of Italy 6-0, 6-2 for a place against Dementieva Friday.
"We have only a few tournaments in Japan and I'm really glad that I could reach the quarter-finals and draw people's attention on my home ground," said Asagoe, ranked 32nd against Vinci's 116.
"This is a big step forward to my next stage, but you should reduce her errors to move up further. I think I've improved enough to reduce errors and try to hit a winner."
Russian sixth seed Elena Likhovtseva had a hard time beating former Japan Open champion Jill Craybas of the United States 7-5, 4-6, 6-2, to book a place against Wimbledon champion Maria Sharapova of Russia, second seed.
RESULTS (x denotes seeds):
Singles (2nd round): Shinobu Asagoe (JPN) bt Roberta Vinci (ITA) 6-0, 6-2; Elena Dementieva (RUS x4) bt Akiko Morigami (JPN) 6-2, 6-2; Lindsay Davenport (USA x1) bt Saori Obata (JPN) 6-4, 6-3; Elena Likhovtseva (RUS x6) bt Jill Craybas (USA) 7-5, 4-6, 6-2.