Davydenko, a former world number three but now ranked 40th, won the title in his home city in 2004, 2006 and 2007 but went down 7-5 6-4 to Bogomolov.
The 29-year-old, who reached the quarter-finals last year, said on www.atpworldtour.com: "It was emotionally tough on both of us, especially playing in our homeland.
"I was very aggressive to end the first set and then went up 4-0 in the second set. Again, Nikolay displayed some great tennis from the back of the court and was able to climb back to 4-4. I kept my composure and I think that was the main reason I was able to pull it out."
Argentinian seventh seed Carlos Berlocq ended the hopes of another Russian, Andrey Kuznetsov, recovering from a poor start to win 1-6 6-4 6-3 while there were also wins for Igor Sijsling and home qualifier Konstantin Kravchuk.
The defending champion in the women's tournament, Dominika Cibulkova, dropped the first set against Russia's Ekaterina Makarova but the fifth seed hit back to win 2-6 6-4 6-2.
In a late-night epic, Romania's Simona Halep defeated sixth seed Nadia Petrova 3-6 7-5 7-5. The match took three hours and eight minutes and finished just after 12.30am.
Alize Cornet, Vesna Dolonc, Tsvetana Pironkova and Yaroslava Shvedova also made it through to the second round.