Andreev, who reached a career-high ranking of No. 18 in 2008, has dropped to No. 115 and hasn't made it to a quarterfinal this season. He will decide his future in tennis later this year.
"You cannot beat anyone playing on one leg," he said.
On Monday, he broke twice to win the first set. But Seppi, ranked 53rd, made one break in the second set and one more early in the third to serve for the match at 1-1 and 5-4 up. But the Russian broke back to force a tiebreaker.
"A tiebreaker is always a lottery," Andreev said. "I made a couple of mistakes, then narrowed the gap to 5-4 down but luck was on his side."
Dushevina was down 4-0 in the first set and 4-2 in the second before winning four consecutive games to wrap up the match.
"It was a tough match and I was trailing in both sets," Dushevina said. "But I managed to turn my luck."
Also in the women's first round, Estonia's Kaia Kanepi defeated Italy's Sara Errani 6-0, 7-5; Nadia Petrova beat fellow wild card Evgeniya Rodina 6-4, 7-6 (3) in an all-Russian match; and Serbia's Bojana Jovanovski ousted Ukraine's Alona Bondarenko 6-3, 6-0.
In the men's opener, Teymuraz Gabashvili of Russia advanced to the second round with a 6-2, 6-4 victory over Karol Beck of Slovakia; Pere Riba of Spain beat Andreas Haider-Maurer of Austria 6-2, 6-7 (1), 6-3; and Mikhail Kukushkin of Kazakhstan defeated Lukas Rosol of the Czech Republic 7-6 (5), 7-5.
Zvonareva is among the seven players who have already qualified for next week's season-ending WTA Tour championships in Istanbul. Second-seeded Agnieszka Radwanska, who won the China Open in Beijing a week ago for her second straight title and third of the season, needs to win just one match in Moscow to secure the last spot in the championships.