Davydenko was in charge in the first set but Bedene came back with three breaks to even the match at a set apiece. Bedene dropped just eight points over five games serving in the third set and finished off one of his two break chances to earn a spot in the second round.
No 7-seeded Viktor Troicki rallied for a 3-6, 6-3, 6-4 win over Michael Russell. Troicki was 0-for-3 in saving break points in the first set but lost his serve only once the rest of the match.
Grega Zemlja also came from behind to get past David Goffin 5-7, 6-0, 6-2. He won about two-thirds of the points over the last two sets.
Igor Sijsling took out Evgeny Korolev 6-2, 6-4 in 56 minutes. Sijsling won 70 percent of the points when serving and didn't face a break point.
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
Duggar sisters unveil Christian dating rules in new book