Federer, the defending champion, booked his place in the last eight with 6-3, 6-4 win over Marcel Granollers, while Davydenko, who defeated the Swiss in the semi-finals of the 2009 ATP World Tour Finals in London, ousted Victor Hanescu 6-4, 7-6.
A former world No 3, Davydenko has slipped to No 46 in the world rankings now and is suffering from a crisis of confidence, but Federer knows what the 31 year old is capable of and will not be taking the match lightly.
"He's obviously still a great ball striker," Federer, who has an 18-2 record against Davydenko, said after his second round win.
"I'll never, you know, disrespect a guy like Nikolay. He's done too much in the game. That's why I know it's a dangerous round next match.
"And then it almost doesn't matter what he has done in the past. I know what he can do on his absolute best day because I was one of the guys that got crushed by him as well during that time. I expect him to come out and play that way."
Having been stretched to three sets in his opening match by the wild card Malek Jaziri, Federer looked a lot sharper last night, commanding the points against Granollers, a player he had defeated by an identical score in their only previous meeting, in 2011 in Dubai.
Federer, a five-time Dubai champion, took the first set in 26 minutes.
The Swiss then went a break-upp in the fifth game of the second set and had two match points as Granollers served at 3-5, but the Spaniard managed to extend the match by another game.
"I'm happy I bounced back after a rough opening first set here in the first round," Federer, the world No 2, said.
"I think I was sharper today. I had a more clear plan now.
"I knew what I could and couldn't do. I was a bit more confident overall … I knew what I wanted to do and I was able to do it, so I'm happy."
Novak Djokovic, the world No 1 and top seed, also booked his place in the quarter-finals with a comfortable 6-1, 7-6 win over Roberto Bautista Agut in the second match of the night.
"It was good match to be a part of," Djokovic said.
"It did get very exciting towards the end. The crowd got into it and it was not easy to finish. He put up a great fight. I had never played him before, but he is a great competitor."
The three-time Dubai champion now meets the Italian Andreas Seppi today.
He said: "He is also one of those competitive guys. He has been on the tour for many years, featuring consistently among the top 30 or 40 guys.
"He can play on different surfaces consistently well and I will have to earn my win again."
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