Federer was on imperious form against the 19-year-old as the Swiss set up a clash with American Mardy Fish, who defeated Czech Radek Stepanek 6-3 6-3 in a repeat of the 2010 final in Ohio.
"It's his kind of surface, he's at home in America and so I am going to have my hands full," Federer said of Fish, who is the last American standing in Cincinnati.
Djokovic's late match on Center Court was curtailed with barely half an hour on the clock as Davydenko threw in the towel, citing a shoulder problem.
Russian Davydenko, clearly hampered by the injury, had lost the first set 6-0 after an awful display of serving which saw him notch up eight double faults in his three service games.
"It's never nice to win like that, it was obvious that he had problems as he wasn't able to serve over 90 miles per hour," Djokovic said.
The Serbian world number two now meets Marin Cilic for a place in the semis, the Croat having progressed with a 7-6(4) 6-2 win over Spain's Pablo Andujar.
Argentine Juan Martin del Potro fought past Serb Viktor Troicki 7-6 2-6 6-1 to set up a meeting with Jeremy Chardy, who stunned Olympic champion Andy Murray 6-4 6-4.
There were fears that the Argentine player would not even be able to complete the first set when he called a medical time-out after only his first service game because of a problem with his left wrist.
In spite of those struggles he actually claimed the first break of the set in the third game, only for Troicki to respond in kind in the very next game.
Del Potro was clearly avoiding using his left hand whenever possible, but he managed to recover in time to win the tie-break 7-2 after an hour-and-a-quarter.
Troicki had never before claimed a set against Del Potro in their three previous meetings on hardcourt, but he stepped up his game to comfortably level by taking the second 6-2.
The world number 32 failed to make the transition into the third set with that form, however, and Del Potro appeared to leave his wrist injury behind him by taking the decider 6-1.
Completing the quarter-final line-up is Milos Raonic, who will play Stanislas Wawrinka.
Big-serving Canadian Raonic sent fifth seed Tomas Berdych packing from the tournament in Mason with a 6-4 2-6 6-2 victory, while Wawrinka saw off the challenge of Kei Nishikori, the Japanese 14th seed, 6-3 6-3.