Davydenko reached the quarterfinals by beating fourth-seeded Mikhail Youzhny 7-5, 6-3. He was joined by Monfils, who upset third-seeded Philipp Kohlschreiber 6-4, 2-6, 6-4.
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
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
"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."