World number two Djokovic raced to a 6-1 6-3 win over Roberto Bautista Agut of Spain in just 57 minutes.
The Serbian top seed opened up a 5-0 lead in the opening set before Agut managed to eventually get on the scoreboard.
The second set was a similar story and, despite dropping his serve while serving for the match at 5-2 up, Djokovic closed out the set and the match with a break of his own in the next game.
''I have done really well today from the first to the last point,'' Djokovic said. ''There was no major ups and downs, especially with the serve that helped me to win comfortably my service games, a lot of free points.''
Djokovic next plays sixth-seeded Mikhail Youzhny, who ended the hopes of British wildcard James Ward 6-1 7-6 (3).
Federer meanwhile was made to work hard for a 6-2 6-7(4) 6-3 win over Radek Stepanek as the Swiss maestro's serve let him down.
''I got broken four times which is difficult, but it's good to win those type of matches,'' said Federer, who faced eight break points against his serve. ''I'm happy to get through.
''It didn't look good there for a while, but I got it done.''
Federer will now play another Czech, Lukas Rosol, for a semi-final berth after his 6-4 7-6 (4) upset of Dmitry Tursunov.
''Today was quite frustrating,'' Federer added. ''I had momentum on my side at the beginning, but it was tough to keep it going.
''After the first set I was under pressure the entire match.''
Elsewhere, third seed Tomas Berdych romped past Sergiy Stakhovsky of Ukraine 6-2 6-1, while fifth seeded Jo-Wilfried Tsonga was handed a walkover in his match with Nikolay Davydenko after the Russian withdrew before a ball was hit with a rib injury.
Berdych and Tsonga will now meet in a mouth-watering quarter-final.
''I was working a little more on my return stats than on my service stats,'' Berdych said. ''The main focus really for the next days is to get my percentage of the first serve back and really find a nice and sweet rhythm for my serve.''
Dubai Championships results
1-Novak Djokovic (Serbia) beat Roberto Bautista (Spain) 6-1 6-3
3-Tomas Berdych (Czech Republic) beat Sergiy Stakhovsky (Ukraine) 6-2 6-1
4-Roger Federer (Switzerland) beat Radek Stepanek (Czech Republic) 6-2 6-7(4) 6-3
5-Jo-Wilfried Tsonga (France) beat Nikolay Davydenko (Russia) WO
6-Mikhail Youzhny (Russia) beat James Ward (Britain) 6-1 7-6(3)
Lukas Rosol (Czech Republic) beat 8-Dmitry Tursunov (Russia) 6-4 7-6(4)
7-Philipp Kohlschreiber (Germany) beat Andreas Seppi (Italy) 6-3 6-3
Malek Jaziri (Tunisia) beat Somdev Devvarman (India) 6-3 7-5
- Sports & Recreation
- Roberto Bautista Agut
- Tomas Berdych