Bedene replaced Dmitry Tursunov of Russia in the main draw and needed less than 2 hours to add to Davydenko's opening-round losses in Munich, Madrid and Rome.
Seventh-seeded Viktor Troicki defeated Michael Russell of the United States. The Serb will play Grega Zemlja of Slovenia, who saved 13 of 15 breakpoints to beat David Goffin of Belgium 5-7, 6-0, 6-2.
Igor Sijsling of the Netherlands defeated Kazakh qualifier Evgeny Korolev 6-2, 6-4, serving 15 aces in his first clay match of the season. He will meet Philipp Kohlschreiber of Germany.
Results from the third day of the Dusseldorf Cup ATP tournament (x denotes seed):
First Round:
Grega Zemlja (SLO) bt David Goffin (BEL) 5-7, 6-0, 6-2
Igor Sijsling (NED) bt Evgeny Korolev (KAZ) 6-2, 6-4