Top-seeded David Ferrer beat Germany qualifier Tobias Kamke 6-3, 6-2. Second-seeded Richard Gasquet rallied past 55th-ranked Grega Zemlja of Slovenia 6-7 (7), 6-4, 7-6 in a match that lasted nearly 3 hours.
Davydenko, once ranked as high as No. 3, combined a consistent first serve with aggressive play to unnerve the 25th-ranked Youzhny.
Davydenko broke his opponent to take a 6-5 lead in the first set and won when Youzhny hit a forehand into the net. Davydenko kept the momentum going into the second set, forcing Youzhny to save a break point in the first and third games. At 2-2, Davydenko won three straight games to take control.
"Tough match," said Davydenko, who won the tournament in Doha three years ago. "Maybe we didn't start well with so many mistakes. I know against Russians when you play in second round, it's not easy."
The 44th-ranked Davydenko said he was targeting a place in the top 20 this year after failing to win a tournament in 2012.
"If I really concentrate and (practice) and play, I want to see results," Davydenko said.
Monfils, who has fallen to 77th in the rankings after knee troubles forced him to cut short his 2012 season, used his powerful service game to take the lead. But in the second set, the Frenchman appeared frazzled by a new rule that requires players to serve in 25 seconds.
Monfils repeatedly argued with the umpire after getting a warning that he was taking too long. Soon, Kohlschreiber had a 5-1 lead.
In the third set, Monfils served four of his 10 aces and Kohlschreiber started making more unforced errors. The German also missed three early chances to break Monfils.
"It's always good to have a great victory like this under your belt," Monfils said. "Physically, I'm happy because I served very fast and there was no pain, so I was pleased with that. At the end of the match, I was very aggressive and made the shots, so I was happy with that."